Package 'GLDEX'

Description

The fitting algorithms considered in this package have two major objectives. One is to provide a smoothing device to fit distributions to data using the weight and unweighted discretised approach based on the bin width of the histogram. The other is to provide a definitive fit to the data set using the maximum likelihood estimation.

Copyright Information: To ensure the stability of this package, this package ports other functions from other open sourced packages directly so that any changes in other packages will not cause this package to malfunction.

All functions obtained from other sources have been acknowledged by the author in the authorship or the description sections of the help files and they are freely available online for all to use. Please contact the author for any copyright issues.

Specifically the following functions have been modified from R:

hist.su, ks.gof, pretty.su

The following functions are taken from other open source packages in R:

runif.pseudo, rnorm.pseudo, runif.halton, rnorm.halton, runif.sobol, rnorm.sobol by Diethelm Wuertz distributed under GPL.

digitsBase, QUnif and sHalton written by Martin Maechler distributed under GPL.

dgl, pgl, rgl, qgl, starship.adpativegrid, starship.obj and starship written by Robert King and some functions modified by Steve Su distributed under GPL.

Lmoments and t1lmoments written by Juha Karvanen distributed under GPL.

Details

This package allows a direct fitting method onto the data set using fun.RMFMKL.ml, fun.RMFMKL.ml.m, fun.RMFMKL.hs, fun.RMFMKL.hs.nw, fun.RPRS.ml, fun.RPRS.ml.m, fun.RPRS.hs, fun.RPRS.hs.nw, fun.RMFMKL.qs, fun.RPRS.qs, fun.RMFMKL.mm, fun.RPRS.mm, fun.RMFMKL.lm, fun.RPRS.lm and in the case of bimodal data set: fun.auto.bimodal.qs, fun.auto.bimodal.ml, fun.auto.bimodal.pml functions. The resulting fits can be graphically gauged by fun.plot.fit or fun.plot.fit.bm (for bimodal data), or examined by numbers using the Kolmogorov-Smirnoff resample tests (fun.diag.ks.g) and fun.diag.ks.g.bimodal). For unimodal data fits, it is also possible to compare the mean, variance, skewness and kurtosis of the fitted distribution with the data set using fun.comp.moments.ml and fun.comp.moments.ml.2 functions. Similarly, for bimodal data fits, this is done via fun.theo.bi.mv.gld and fun.moments.r. Additionally, L moments for single generalised lambda distribution can be obtained using fun.lm.theo.gld. For graphical display of goodness of fit, quantile plots can be used, these can be done using qqplot.gld and qqplot.gld.bi for univariate and bimodal generalised lambda distribution fits respectively.

Author(s)

Steve Su <[email protected]>

References

Asquith, W. (2007), L-moments and TL-moments of the generalized lambda distribution, Computational Statistics and Data Analysis 51(9): 4484-4496.

Freimer, M., Mudholkar, G. S., Kollia, G. & Lin, C. T. (1988), A study of the generalized tukey lambda family, Communications in Statistics - Theory and Methods *17*, 3547-3567.

Gilchrist, Warren G. (2000), Statistical Modelling with Quantile Functions, Chapman & Hall

Karian, Z.A., Dudewicz, E.J., and McDonald, P. (1996), The extended generalized lambda distribution system for fitting distributions to data: history, completion of theory, tables, applications, the “Final Word” on Moment fits, Communications in Statistics - Simulation and Computation *25*, 611-642.

Karian, Zaven A. and Dudewicz, Edward J. (2000), Fitting statistical distributions: the Generalized Lambda Distribution and Generalized Bootstrap methods, Chapman & Hall

Karvanen, J. and A. Nuutinen (2008), Characterizing the generalized lambda distribution by L-moments, Computational Statistics and Data Analysis 52(4): 1971-1983. doi:10.1016/j.csda.2007.06.021

King, R.A.R. & MacGillivray, H. L. (1999), A starship method for fitting the generalised lambda distributions, Australian and New Zealand Journal of Statistics, 41, 353-374 doi:10.1111/1467-842X.00089

Ramberg, J. S. & Schmeiser, B. W. (1974), An approximate method for generating asymmetric random variables, Communications of the ACM *17*, 78-82.

Su, S. (2005). A Discretized Approach to Flexibly Fit Generalized Lambda Distributions to Data. Journal of Modern Applied Statistical Methods (November): 408-424. doi:10.22237/jmasm/1130803560

Su, S. (2007). Nmerical Maximum Log Likelihood Estimation for Generalized Lambda Distributions. Computational Statistics and Data Analysis: *51*, 8, 3983-3998. doi:10.1016/j.csda.2006.06.008

Su, S. (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9. doi:10.18637/jss.v021.i09

Su, S. (2009). Confidence Intervals for Quantiles Using Generalized Lambda Distributions. Computational Statistics and Data Analysis *53*, 9, 3324-3333. doi:10.1016/j.csda.2009.02.014

Su, S. (2010). Chapter 14: Fitting GLDs and Mixture of GLDs to Data using Quantile Matching Method. Handbook of Distribution Fitting Methods with R. (Karian and Dudewicz) 557-583. doi:10.1201/b10159-3

Su, S. (2010). Chapter 15: Fitting GLD to data using GLDEX 1.0.4 in R. Handbook of Distribution Fitting Methods with R. (Karian and Dudewicz) 585-608. doi:10.1201/b10159-3

Su, S. (2015) "Flexible Parametric Quantile Regression Model" Statistics & Computing 25 (3). 635-650. doi:10.1007/s11222-014-9457-1

Su S. (2021) "Flexible parametric accelerated failure time model" J Biopharm Stat. 2021 Sep 31(5):650-667. doi:10.1080/10543406.2021.1934854

See Also

GLDreg package in R for GLD regression models.

Examples

###Univariate distributions example:

set.seed(1000)

junk<-rweibull(300,3,2)

##A faster ML estimtion 

junk.fit1<-fun.RMFMKL.ml.m(junk)
junk.fit2<-fun.RPRS.ml.m(junk)

qqplot.gld(junk.fit1,data=junk,param="fmkl")
qqplot.gld(junk.fit2,data=junk,param="rs")

##Using discretised approach, with 50 classes

#Using discretised method with weights
obj.fit1.hs<-fun.data.fit.hs(junk)

#Plot the resulting fit. The fun.plot.fit function also works for singular fits 
#such as those by fun.plot.fit(obj.fit1.ml,junk,nclass=50,
#param=c("rs","fmkl","fmkl"),xlab="x")

fun.plot.fit(obj.fit1.hs,junk,nclass=50,param=c("rs","fmkl"),xlab="x")

#Compare the mean, variance, skewness and kurtosis of the fitted distribution 
#with actual data

fun.theo.mv.gld(obj.fit1.hs[1,1],obj.fit1.hs[2,1],obj.fit1.hs[3,1],
obj.fit1.hs[4,1],param="rs")
fun.theo.mv.gld(obj.fit1.hs[1,2],obj.fit1.hs[2,2],obj.fit1.hs[3,2],
obj.fit1.hs[4,2],param="fmkl")
fun.moments.r(junk)

#Conduct resample KS tests
fun.diag.ks.g(obj.fit1.hs[,1],junk,param="rs")
fun.diag.ks.g(obj.fit1.hs[,2],junk,param="fmkl")

##Try another fit, say 15 classes

obj.fit2.hs<-fun.data.fit.hs(junk,rs.default="N",fmkl.default="N",no.c.rs = 15, 
no.c.fmkl = 15)

fun.plot.fit(obj.fit2.hs,junk,nclass=50,param=c("rs","fmkl"),xlab="x")

fun.theo.mv.gld(obj.fit2.hs[1,1],obj.fit2.hs[2,1],obj.fit2.hs[3,1],
obj.fit2.hs[4,1],param="rs")
fun.theo.mv.gld(obj.fit2.hs[1,2],obj.fit2.hs[2,2],obj.fit2.hs[3,2],
obj.fit2.hs[4,2],param="fmkl")
fun.moments.r(junk)

fun.diag.ks.g(obj.fit2.hs[,1],junk,param="rs")
fun.diag.ks.g(obj.fit2.hs[,2],junk,param="fmkl")

##Uses the maximum likelihood estimation method

#Fit the function using fun.data.fit.ml
obj.fit1.ml<-fun.data.fit.ml(junk)

#Plot the resulting fit
fun.plot.fit(obj.fit1.ml,junk,nclass=50,param=c("rs","fmkl","fmkl"),xlab="x",
name=".ML")

#Compare the mean, variance, skewness and kurtosis of the fitted distribution 
#with actual data
fun.comp.moments.ml(obj.fit1.ml,junk)

#Do a quantile plot

qqplot.gld(junk,obj.fit1.ml[,1],param="rs",name="RS ML fit")

#Run a KS resample test on the resulting fit

fun.diag2(obj.fit1.ml,junk,1000)

#It is possible to use say fun.data.fit.ml(junk,rs.leap=409,fmkl.leap=409,
#FUN="QUnif") to find solution under a different set of low discrepancy number 
#generators.

###Bimodal distributions example:

#Fitting mixture of generalised lambda distributions on the data set using both 
#the maximum likelihood and partition maximum likelihood and plot the resulting 
#fits

opar <- par() 
par(mfrow=c(2,1))

junk<-fun.auto.bimodal.ml(faithful[,1],per.of.mix=0.01,clustering.m=clara,
init1.sel="rprs",init2.sel="rmfmkl",init1=c(-1.5,1.5),init2=c(-0.25,1.5),
leap1=3,leap2=3)
fun.plot.fit.bm(nclass=50,fit.obj=junk,data=faithful[,1],
name="Maximum likelihood using",xlab="faithful1",param.vec=c("rs","fmkl"))

#Do a quantile plot

qqplot.gld.bi(faithful[,1],junk$par,param1="rs",param2="fmkl",
name="RS FMKL ML fit",range=c(0.001,0.999))

par(opar)

junk<-fun.auto.bimodal.pml(faithful[,1],clustering.m=clara,init1.sel="rprs",
init2.sel="rmfmkl",init1=c(-1.5,1.5),init2=c(-0.25,1.5),leap1=3,leap2=3)
fun.plot.fit.bm(nclass=50,fit.obj=junk,data=faithful[,1],
name="Partition maximum likelihood using",xlab="faithful1",
param.vec=c("rs","fmkl"))

#Fit the faithful[,1] data from the dataset library using sobol sequence 
#generator for the first distribution fit and halton sequence for the second 
#distribution fit.

fit1<-fun.auto.bimodal.ml(faithful[,1],init1.sel="rmfmkl",init2.sel="rmfmkl",
init1=c(-0.25,1.5),init2=c(-0.25,1.5),leap1=3,leap2=3,fun1="runif.sobol",
fun2="runif.halton")

#Run diagnostic KS tests

fun.diag.ks.g.bimodal(fit1$par[1:4],fit1$par[5:8],prop1=fit1$par[9],
data=faithful[,1],param1="fmkl",param2="fmkl")

#Find the theoretical moments of the fit

fun.theo.bi.mv.gld(fit1$par[1],fit1$par[2],fit1$par[3],fit1$par[4],"fmkl",
fit1$par[5],fit1$par[6],fit1$par[7],fit1$par[8],"fmkl",fit1$par[9])

#Compare this with the empirical moments from the data set.

fun.moments.r(faithful[,1])

#Do a quantile plot

qqplot.gld.bi(faithful[,1],fit1$par,param1="fmkl",param2="fmkl",
name="FMKL FMKL ML fit")

#Quantile matching method

#Fitting faithful data from the dataset library, with the clara clustering 
#regime. The first distribution is RS and the second distribution is fmkl. 
#The percentage of data mix is 1%.

#Fitting normal(3,2) distriution using the default setting
junk<-rnorm(50,3,2)
fun.data.fit.qs(junk)

fun.auto.bimodal.qs(faithful[,1],per.of.mix=0.01,clustering.m=clara,
init1.sel="rprs",init2.sel="rmfmkl",init1=c(-1.5,1,5),init2=c(-0.25,1.5),
leap1=3,leap2=3)

#L Moment matching

#Fitting normal(3,2) distriution using the default setting
junk<-rnorm(50,3,2)
fun.data.fit.lm(junk)

# Moment matching method

#Fitting normal(3,2) distriution using the default setting
junk<-rnorm(50,3,2)
fun.data.fit.mm(junk)

# Example on fitting mixture of normal distributions

data1<-c(rnorm(1500,-1,2/3),rnorm(1500,1,2/3))

junk<-fun.auto.bimodal.ml(data1,per.of.mix=0.01,clustering.m=data1>0,
init1.sel="rprs",init2.sel="rmfmkl",init1=c(-1.5,1.5),init2=c(-0.25,1.5),
leap1=3,leap2=3)

fun.plot.fit.bm(nclass=50,fit.obj=junk,data=data1,
name="Maximum likelihood using",xlab="faithful1",param.vec=c("rs","fmkl"))

qqplot.gld.bi(data1,junk$par,param1="rs",param2="fmkl",
name="RS FMKL ML fit",range=c(0.001,0.999))

# Generate random observations from FMKL generalised lambda distributions with 
# parameters (1,2,3,4) and (4,3,2,1) with 50% of data from each distribution.
fun.simu.bimodal(c(1,2,3,4),c(4,3,2,1),prop1=0.5,param1="fmkl",param2="fmkl")

Description

Integer number representations in other Bases.

Formally, for every element $N =$x[i], compute the (vector of) “digits” $A$ of the base $b$ representation of the number $N$, $N = \sum_{k=0}^M A_{M-k} b ^ k$.
Revert such a representation to integers.

Usage

digitsBase(x, base = 2, ndigits = 1 + floor(log(max(x), base)))

Arguments

Value

For digitsBase(), an object, say m, of class "basedInt" which is basically a (ndigits x n) matrix where m[,i] corresponds to x[i], n <- length(x) and attr(m,"base") is the input base.

as.intBase() and the as.integer method for basedInt objects return an integer vector.

Note

digits and digits.v are now deprecated and will be removed from the sfsmisc package.

Author(s)

Martin Maechler, Dec 4, 1991 (for S-plus; then called digits.v).

Examples

digitsBase(0:12, 8) #-- octal representation

## This may be handy for just one number (and default decimal):
digits <- function(n, base = 10) as.vector(digitsBase(n, base = base))
digits(128, base = 8) # 2 0 0

## one way of pretty printing (base <= 10!)
b2ch <- function(db)
        noquote(gsub("^0+(.{1,})$"," \1", apply(db, 2, paste, collapse = "")))
b2ch(digitsBase(0:33, 2))  #->  0 1 10 11 100 101 ... 100001
b2ch(digitsBase(0:33, 4))  #->  0 1 2 3 10 11 12 13 20 ... 200 201

## Hexadecimal:
i <- c(1:20, 100:106)
M <- digitsBase(i, 16)
hexdig <- c(0:9, LETTERS[1:6])
cM <- hexdig[1 + M]; dim(cM) <- dim(M)
b2ch(cM) #->  1  2  3  4  5  6  7  8  9  A  B  C  D  E  F 10 11 ... 6A

Description

This function will fit mixture of generalised lambda distributions to dataset. It is restricted to two generalised lambda distributions. The method of fitting is maximum likelihood via EM algorithm. It is a two step optimization procedure, each unimodal part of the bimodal distribution is modelled using the maximum likelihood method or the starship method (FMKL GLD only), these initial values are the used to maximise the likelihood for the entire bimodal distribution using the EM algorithm. It fits mixture of the form p*(f1)+(1-p)*(f2) where f1 and f2 are pdfs of the generalised lambda distributions.

Usage

fun.auto.bimodal.ml(data, per.of.mix = 0.01, clustering.m = clara, 
init1.sel = "rprs", init2.sel = "rprs", init1=c(-1.5, 1.5), init2=c(-1.5, 1.5), 
leap1=3, leap2=3,fun1="runif.sobol",fun2="runif.sobol",no=10000, max.it=5000,
optim.further="Y")

Arguments

Details

The initial values that work well for RPRS are c(-1.5,1.5) and for RMFMKL are c(-0.25,1.5). For scrambling, if 1, 2 or 3 the sequence is scrambled otherwise not. If 1, Owen type type of scrambling is applied, if 2, Faure-Tezuka type of scrambling, is applied, and if 3, both Owen+Faure-Tezuka type of scrambling is applied. The star method uses the same initial values as rmfmkl since it uses the FMKL generalised lambda distribution. Nelder-Simplex algorithm is used in the numerical optimization. rprs stands for revised percentile method for RS generalised lambda distribution and "rmfmkl" stands for revised method of moment for FMKL generalised lambda distribution. These acronyms represents the initial optimization algorithm used to get a reasonable set of initial values for the subsequent optimization procedues. This function is an improvement from Su (2007) in Journal of Statistical Software.

Value

Note

If the number of observations is small, rprs can sometimes fail as the percentiles may not exist for this data. Also, if the initial values do not span a valid generalised lambda distribution, try another set of initial values.

Author(s)

Steve Su

References

Bratley P. and Fox B.L. (1988) Algorithm 659: Implementing Sobol's quasi random sequence generator, ACM Transactions on Mathematical Software 14, 88-100.

Joe S. and Kuo F.Y. (1998) Remark on Algorithm 659: Implementing Sobol's quasi random Sequence Generator.

Nelder, J. A. and Mead, R. (1965) A simplex algorithm for function minimization. Computer Journal *7*, 308-313.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.auto.bimodal.pml, fun.plot.fit.bm, fun.diag.ks.g.bimodal

Examples

# Fitting faithful data from the dataset library, with the clara clustering 
# regime. The first distribution is RS and the second distribution is fmkl. 
# The percentage of data mix is 1%.

fun.auto.bimodal.ml(faithful[,1],per.of.mix=0.01,clustering.m=clara,
init1.sel="rprs",init2.sel="rmfmkl",init1=c(-1.5,1,5),init2=c(-0.25,1.5),
leap1=3,leap2=3)

Description

This function will fit mixture of generalised lambda distributions to dataset. It is restricted to two generalised lambda distributions. The method of fitting is parition maximum likelihood. It is a two step optimization procedure, each unimodal part of the bimodal distribution is modelled using the maximum likelihood method or the starship method (FMKL GLD only). These initial values the used to "maximise" the complete log likelihood for the entire bimodal distribution. It fits mixture of the form p*(f1)+(1-p)*(f2) where f1 and f2 are pdfs of the generalised lambda distributions.

Usage

fun.auto.bimodal.pml(data, clustering.m = clara, init1.sel = "rprs", 
init2.sel = "rprs", init1=c(-1.5, 1.5), init2=c(-1.5, 1.5), leap1=3, leap2=3,
fun1="runif.sobol", fun2="runif.sobol",no=10000,max.it=5000, optim.further="Y")

Arguments

Details

The initial values that work well for RPRS are c(-1.5,1.5) and for RMFMKL are c(-0.25,1.5). For scrambling, if 1, 2 or 3 the sequence is scrambled otherwise not. If 1, Owen type type of scrambling is applied, if 2, Faure-Tezuka type of scrambling, is applied, and if 3, both Owen+Faure-Tezuka type of scrambling is applied. The star method uses the same initial values as rmfmkl since it uses the FMKL generalised lambda distribution. Nelder-Simplex algorithm is used in the numerical optimization. rprs stands for revised percentile method for RS generalised lambda distribution and "rmfmkl" stands for revised method of moment for FMKL generalised lambda distribution. These acronyms represents the initial optimization algorithm used to get a reasonable set of initial values for the subsequent optimization procedues. This function is an improvement from Su (2007) in Journal of Statistical Software.

Value

Note

If the number of observations is small, rprs can sometimes fail as the percentiles may not exist for this data. Also, if the initial values do not result in a valid generalised lambda distribution, try another set of initial values.

References

Bratley P. and Fox B.L. (1988) Algorithm 659: Implementing Sobol's quasi random sequence generator, ACM Transactions on Mathematical Software 14, 88-100.

Joe S. and Kuo F.Y. (1998) Remark on Algorithm 659: Implementing Sobol's quasi random Sequence Generator.

Nelder, J. A. and Mead, R. (1965) A simplex algorithm for function minimization. Computer Journal *7*, 308-313.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.auto.bimodal.ml,fun.plot.fit.bm, fun.diag.ks.g.bimodal

Examples

# Fitting faithful data from the dataset library, with the clara clustering 
# regime. The first distribution is RS and the second distribution is fmkl. 

fun.auto.bimodal.pml(faithful[,1],clustering.m=clara,init1.sel="rprs",
init2.sel="rmfmkl",init1=c(-1.5,1,5),init2=c(-0.25,1.5),leap1=3,leap2=3)

Description

This function will fit mixture of generalised lambda distributions to dataset. It is restricted to two generalised lambda distributions. The method of fitting is quantile matching method. It is a two step optimization procedure, each unimodal part of the bimodal distribution is modelled using quantile matching method. The initial values obtained are then used to maximise the theoretical and empirical quantile match for the entire bimodal distribution. It fits mixture of the form p*(f1)+(1-p)*(f2) where f1 and f2 are pdfs of the generalised lambda distributions.

Usage

fun.auto.bimodal.qs(data, per.of.mix = 0.01, clustering.m = clara, 
init1.sel = "rprs", init2.sel = "rprs", init1=c(-1.5, 1.5), init2=c(-1.5, 1.5), 
leap1=3, leap2=3, fun1 = "runif.sobol", fun2 = "runif.sobol", trial.n = 100, 
len = 1000, type = 7, no = 10000, maxit = 5000)

Arguments

Details

The initial values that work well for RPRS are c(-1.5,1.5) and for RMFMKL are c(-0.25,1.5). For scrambling, if 1, 2 or 3 the sequence is scrambled otherwise not. If 1, Owen type type of scrambling is applied, if 2, Faure-Tezuka type of scrambling, is applied, and if 3, both Owen+Faure-Tezuka type of scrambling is applied. The star method uses the same initial values as rmfmkl since it uses the FMKL generalised lambda distribution. Nelder-Simplex algorithm is used in the numerical optimization. rprs stands for revised percentile method for RS generalised lambda distribution and "rmfmkl" stands for revised method of moment for FMKL generalised lambda distribution. These acronyms represents the initial optimization algorithm used to get a reasonable set of initial values for the subsequent optimization procedues.

Value

Note

If the number of observations is small, rprs can sometimes fail as the percentiles may not exist for this data. Also, if the initial values do not span a valid generalised lambda distribution, try another set of initial values.

Author(s)

Steve Su

References

Bratley P. and Fox B.L. (1988) Algorithm 659: Implementing Sobol's quasi random sequence generator, ACM Transactions on Mathematical Software 14, 88-100.

Joe S. and Kuo F.Y. (1998) Remark on Algorithm 659: Implementing Sobol's quasi random Sequence Generator.

Nelder, J. A. and Mead, R. (1965) A simplex algorithm for function minimization. Computer Journal *7*, 308-313.

Su (2008). Fitting GLD to data via quantile matching method. (Book chapter to appear)

See Also

fun.auto.bimodal.pml, fun.auto.bimodal.ml, fun.plot.fit.bm, fun.diag.ks.g.bimodal

Examples

# Fitting faithful data from the dataset library, with the clara clustering 
# regime. The first distribution is RS and the second distribution is fmkl. 
# The percentage of data mix is 1%.

fun.auto.bimodal.qs(faithful[,1],per.of.mix=0.01,clustering.m=clara,
init1.sel="rprs",init2.sel="rmfmkl",init1=c(-1.5,1,5),init2=c(-0.25,1.5),
leap1=3,leap2=3)

Description

This is the secondary optimization procedure to evaluate the final bimodal distribution fits using the maximum likelihood. It usually relies on initial values found by fun.bimodal.init function.

Usage

fun.bimodal.fit.ml(data, first.fit, second.fit, prop, param1, param2, selc1, 
selc2)

Arguments

Details

This function should be used in tandem with fun.bimodal.init.

Value

Note

There is currently no guarantee of a global convergence.

Author(s)

Steve Su

References

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

link{fun.bimodal.fit.pml}, fun.bimodal.init

Examples

# Extract faithful[,2] into faithful2
 faithful2<-faithful[,2]

 # Uses clara clustering method
 clara.faithful2<-fun.class.regime.bi(faithful2, 0.01, clara)

 # Save into two different objects
 qqqq1.faithful2.cc<-clara.faithful2$data.a
 qqqq2.faithful2.cc<-clara.faithful2$data.b

 # Find the initial values
 result.faithful2.init<-fun.bimodal.init(data1=qqqq1.faithful2.cc,
 data2=qqqq2.faithful2.cc, rs.leap1=3,fmkl.leap1=3,rs.init1 = c(-1.5, 1.5), 
 fmkl.init1 = c(-0.25, 1.5), rs.leap2=3,fmkl.leap2=3,rs.init2 = c(-1.5, 1.5), 
 fmkl.init2 = c(-0.25, 1.5))

 # Find the final fits
 result.faithful2.rsrs<-fun.bimodal.fit.ml(data=faithful2,
 result.faithful2.init[[2]],result.faithful2.init[[3]],
 result.faithful2.init[[1]], param1="rs",param2="rs",selc1="rs",selc2="rs")

 # Output
 result.faithful2.rsrs

Description

This is the secondary optimization procedure to evaluate the final bimodal distribution fits using the partition maximum likelihood. It usually relies on initial values found by fun.bimodal.init function.

Usage

fun.bimodal.fit.pml(data1, data2, first.fit, second.fit, prop, param1, param2, 
selc1, selc2)

Arguments

Details

This function should be used in tandem with fun.bimodal.init function.

Value

Note

There is currently no guarantee of a global convergence.

Author(s)

Steve Su

References

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.bimodal.fit.ml, fun.bimodal.init

Examples

# Extract faithful[,2] into faithful2
 faithful2<-faithful[,2]

 # Uses clara clustering method
 clara.faithful2<-clara(faithful2,2)$clustering

 # Save into two different objects
 qqqq1.faithful2.cc<-faithful2[clara.faithful2==1]
 qqqq2.faithful2.cc<-faithful2[clara.faithful2==2]

 # Find the initial values
 result.faithful2.init<-fun.bimodal.init(data1=qqqq1.faithful2.cc,
 data2=qqqq2.faithful2.cc, rs.leap1=3,fmkl.leap1=3,rs.init1 = c(-1.5, 1.5), 
 fmkl.init1 = c(-0.25, 1.5), rs.leap2=3,fmkl.leap2=3,rs.init2 = c(-1.5, 1.5), 
 fmkl.init2 = c(-0.25, 1.5))

 # Find the final fits
 result.faithful2.rsrs<-fun.bimodal.fit.pml(data1=qqqq1.faithful2.cc,
 data2=qqqq2.faithful2.cc, result.faithful2.init[[2]],
 result.faithful2.init[[3]], result.faithful2.init[[1]],param1="rs",
 param2="rs",selc1="rs",selc2="rs")

 # Output
 result.faithful2.rsrs

Description

After classifying the data using fun.class.regime.bi, this function evaluates the temporary or initial solutions by estimating each part of the bimodal distribution using the maximum likelihood estimation and starship method. These initial solutions are then passed onto fun.bimodal.fit.ml or fun.bimodal.fit.pml to obtain the final fits.

Usage

fun.bimodal.init(data1, data2, rs.leap1, fmkl.leap1, rs.init1, fmkl.init1, 
rs.leap2, fmkl.leap2, rs.init2, fmkl.init2,fun1="runif.sobol",
fun2="runif.sobol",no=10000)

Arguments

Details

All three methods of fitting (RPRS, RMFMKL and STAR) will be given for each part of the bimodal distribution.

Value

Note

This is not designed to be called by the end user explicitly, the difficulties with RPRS parameterisation should be noted by the users.

Author(s)

Steve Su

References

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.class.regime.bi,fun.bimodal.fit.pml, fun.bimodal.fit.ml

Examples

# Split the first column of the faithful data into two using 

 fun.class.regime.bi
 faithful1.mod<-fun.class.regime.bi(faithful[,1], 0.1, clara)

 # Save the datasets
 qqqq1.faithful1.cc1<-faithful1.mod$data.a
 qqqq2.faithful1.cc1<-faithful1.mod$data.b

 # Find the initial values for secondary optimisation.
 
 result.faithful1.init1<-fun.bimodal.init(data1=qqqq1.faithful1.cc1,
 data2=qqqq2.faithful1.cc1, rs.leap1=3,fmkl.leap1=3,rs.init1 = c(-1.5, 1.5), 
 fmkl.init1 = c(-0.25, 1.5), rs.leap2=3,fmkl.leap2=3,rs.init2 = c(-1.5, 1.5), 
 fmkl.init2 = c(-0.25, 1.5))

 # These initial values are then passed onto fun,bimodal.fit.ml to obtain the 
 # final fits.

Description

This function will return a single logical value showing whether a combination of L1, L2, L3 and L4 is a valid GLD.

Usage

fun.check.gld(lambda1, lambda2, lambda3, lambda4, param)

Arguments

Value

A single logical value indicating whether the specified GLD is a valid probability density function

Author(s)

Steve Su

See Also

fun.check.gld.multi

Examples

fun.check.gld(1,4,3,2,"rs")

fun.check.gld(1,4,3,2,"fkml")

fun.check.gld(1,4,3,-2,"rs")

Description

This function will return a logical vector showing whether vector combinations of L1, L2, L3 and L4 are valid GLDs.

Usage

fun.check.gld.multi(l1, l2, l3, l4, param)

Arguments

Details

This is an extension to fun.check.gld

Value

A logical vector indicating whether the specified parameters are valid GLDs

Author(s)

Steve Su

See Also

fun.check.gld

Examples

fun.check.gld.multi(c(1,2,3),c(4,5,6),c(7,8,9),c(10,11,12),param="rs")

fun.check.gld.multi(c(1,2,3),c(4,5,6),c(7,8,9),c(10,11,-12),param="rs")

Description

This function is primarily designed to split a bimodal data vector into two groups to allow the fitting of mixture generalised lambda distributions.

Usage

fun.class.regime.bi(data, perc.cross, fun.cross)

Arguments

Details

This function is part of the routine mixture fitting procedure provided in this package. The perc.cross argument or percentage of cross over is designed to allow the use of maximum likelihood estimation via EM algorithm for fitting bimodal data. When this is invoked, it will ensure both part of the data will contain both the minmum and maximum of the data set as well as a proportion ( specified in perc.cross argument) of observations from each other. If 1% is required, then data.a will contains 1% of the data.b and vice versa after the full data set has been classified into data.a and data.b by the fun.cross classification regime.

Value

Author(s)

Steve Su

References

Kaufman, L. and Rousseeuw, P. J. (1990). Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.

Su (2006) Maximum Log Likelihood Estimation using EM Algorithm and Partition Maximum Log Likelihood Estimation for Mixtures of Generalized Lambda Distributions. Working Paper.

See Also

link{clara}, pam, fanny

Examples

# Classify the faithful[,1] data into two categories with 10% cross over mix.
 fun.class.regime.bi(faithful[,1],0.1,clara)

# Classify the faithful[,1] data into two categories with no mixing:
 fun.class.regime.bi(faithful[,1],0,clara)

Description

After fitting the distribution, it is often desirable to see whether the moments of the data matches with the fitted distribution. This function computes the theoretical and actual moments especially for fun.data.fit.ml function output.

Usage

fun.comp.moments.ml(theo.obj, data, name = "ML")

Arguments

Value

Note

Sometimes it is difficult to find RPRS type of fits to data set, so instead fun.comp.moments.ml.2 is used to compare the theoretical moments of RMFMKL.ML and STAR methods with respect to the dataset fitted.

Author(s)

Steve Su

See Also

fun.comp.moments.ml.2

Examples

# Generate random normally distributed observations.
 junk<-rnorm(1000,3,2)

# Fit the dataset using fun.data.ml
 fit<-fun.data.fit.ml(junk)

# Compare the resulting fits. It is usually the case the maximum likelihood 
# provides better estimation of the moments than the starship method.
 fun.comp.moments.ml(fit,junk)

Description

After fitting the distribution, it is often desirable to see whether the moments of the data matches with the fitted distribution. This function computes the theoretical and actual moments for the FMKL GLD maximum likelihood estimation and starship method.

Usage

fun.comp.moments.ml.2(theo.obj, data, name = "ML")

Arguments

Value

Note

To compare all three fits under fun.data.fit.ml see fun.comp.moments.ml function.

Author(s)

Steve Su

See Also

fun.comp.moments.ml

Examples

## Generate random normally distributed observations.
 junk<-rnorm(1000,3,2)

## Fit the dataset using fun.data.ml
 fit<-cbind(fun.RMFMKL.ml(junk),starship(junk)$lambda)

## Compare the resulting fits. It is usually the case the maximum likelihood 
## provides better estimation of the moments than the starship method.
 fun.comp.moments.ml.2(fit,junk)

Description

This function fits RS and FMKL generalised distribution to data using discretised approach with weights. It is designed to act as a smoother device rather than a definitive fit.

Usage

fun.data.fit.hs(data, rs.default = "Y", fmkl.default = "Y", rs.leap = 3, 
fmkl.leap = 3, rs.init = c(-1.5, 1.5), fmkl.init = c(-0.25, 1.5), no.c.rs = 50, 
no.c.fmkl = 50,FUN="runif.sobol", no=10000)

Arguments

Details

This function optimises the deviations of frequency of the bins to that of the theoretical so it has the effect of "fitting clothes" onto the data set. The user can decide the frequency of the bins they want the distribution to smooth over. The resulting fit may or may not be an adequate fit from a formal statistical point of view such as satisfying the goodness of fit for example, but it can be useful to suggest the range of different distributions exhibited by the data set. The default number of classes calculates the mean and variance after categorising the data into different bins and uses the number of classes that best matches the mean and variance of the original, ungrouped data.The weighting is designed to accentuate the peak or the dense part of the distribution and suppress the tails.

Value

A matrix showing the four parameters of the RS and FMKL distribution fit.

Note

In some cases, the resulting fit may not converge, there are currently no checking mechanism in place to ensure global convergence. The RPRS method can sometimes fail if there are no valid percentiles in the data set or if initial values do not give a valid distribution.

Author(s)

Steve Su

References

Su, S. (2005). A Discretized Approach to Flexibly Fit Generalized Lambda Distributions to Data. Journal of Modern Applied Statistical Methods (November): 408-424.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.RPRS.hs.nw, fun.RMFMKL.hs.nw, fun.RMFMKL.hs, fun.RPRS.hs, fun.data.fit.hs.nw, fun.data.fit.ml

Examples

# Fitting normal(3,2) distriution using the default setting
 junk<-rnorm(1000,3,2)
 fun.data.fit.hs(junk)

Description

This function fits RS and FMKL generalised distribution to data using discretised approach without weights. It is designed to act as a smoother device rather than a definitive fit.

Usage

fun.data.fit.hs.nw(data, rs.default = "Y", fmkl.default = "Y", rs.leap = 3, 
fmkl.leap = 3, rs.init = c(-1.5, 1.5), fmkl.init = c(-0.25, 1.5), no.c.rs = 50, 
no.c.fmkl = 50,FUN="runif.sobol",no=10000)

Arguments

Details

This function optimises the deviations of frequency of the bins to that of the theoretical so it has the effect of "fitting clothes" onto the data set. The user can decide the frequency of the bins they want the distribution to smooth over. The resulting fit may or may not be an adequate fit from a formal statistical point of view such as satisfying the goodness of fit for example, but it can be useful to suggest the range of different distributions exhibited by the data set. The default number of classes calculates the mean and variance after categorising the data into different bins and uses the number of classes that best matches the mean and variance of the original, ungrouped data.

Value

A matrix showing the four parameters of the RS and FMKL distribution fit.

Note

In some cases, the resulting fit may not converge, there are currently no checking mechanism in place to ensure global convergence. The RPRS method can sometimes fail if there are no valid percentiles in the data set or if initial values do not give a valid distribution.

Author(s)

Steve Su

References

Su, S. (2005). A Discretized Approach to Flexibly Fit Generalized Lambda Distributions to Data. Journal of Modern Applied Statistical Methods (November): 408-424.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.RPRS.hs, fun.RMFMKL.hs, fun.RMFMKL.hs.nw, fun.RPRS.hs.nw, fun.data.fit.hs, fun.data.fit.ml

Examples

# Fitting normal(3,2) distriution using the default setting
 junk<-rnorm(1000,3,2)
 fun.data.fit.hs.nw(junk)

Description

This function fits generalised lambda distributions to data using L moment matching method

Usage

fun.data.fit.lm(data, rs.leap = 3, fmkl.leap = 3, rs.init = c(-1.5, 1.5), 
fmkl.init = c(-0.25, 1.5), FUN = "runif.sobol", no = 10000)

Arguments

Details

This function consolidates fun.RPRS.lm and fun.RMFMKL.lm and gives all the fits in one output.

Value

A matrix showing the parameters of RS and FMKL generalised lambda distributions.

Author(s)

Steve Su

References

Asquith, W. (2007). "L-moments and TL-moments of the generalized lambda distribution." Computational Statistics and Data Analysis 51(9): 4484-4496.

Karvanen, J. and A. Nuutinen (2008). "Characterizing the generalized lambda distribution by L-moments." Computational Statistics and Data Analysis 52(4): 1971-1983.

See Also

fun.RPRS.qs, fun.RMFMKL.qs, fun.data.fit.ml, fun.data.fit.hs, fun.data.fit.hs.nw , fun.data.fit.qs, fun.data.fit.mm

Examples

# Fitting normal(3,2) distriution using the default setting
 junk<-rnorm(50,3,2)
 fun.data.fit.lm(junk)

Description

This function fits generalised lambda distributions to data using RPRS, RMFMKL and starship methods.

Usage

fun.data.fit.ml(data, rs.leap = 3, fmkl.leap = 3, rs.init = c(-1.5, 1.5), 
fmkl.init = c(-0.25, 1.5),FUN="runif.sobol",no=10000)

Arguments

Details

This function consolidates fun.RPRS.ml, fun.RMFMKL.ml and starship and gives all the fits in one output.

Value

A matrix showing the parameters of generalised lambda distribution for RPRS, FMFKL and STAR methods.

Note

RPRS can sometimes fail if it is not possible to calculate the percentiles of the data set. This usually happens when the number of data point is small.

Author(s)

Steve Su

References

King, R.A.R. & MacGillivray, H. L. (1999), A starship method for fitting the generalised lambda distributions, Australian and New Zealand Journal of Statistics, 41, 353-374

Su, S. (2007). Numerical Maximum Log Likelihood Estimation for Generalized Lambda Distributions. Computational statistics and data analysis 51(8) 3983-3998.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.RPRS.ml, fun.RMFMKL.ml, starship, fun.data.fit.hs, fun.data.fit.hs.nw , fun.data.fit.qs , fun.data.fit.mm , fun.data.fit.lm

Examples

# Fitting normal(3,2) distriution using the default setting
 junk<-rnorm(50,3,2)
 fun.data.fit.ml(junk)

Description

This function fits generalised lambda distributions to data using moment matching method

Usage

fun.data.fit.mm(data, rs.leap = 3, fmkl.leap = 3, rs.init = c(-1.5, 1.5), 
fmkl.init = c(-0.25, 1.5), FUN = "runif.sobol", no = 10000)

Arguments

Details

This function consolidates fun.RPRS.mm and fun.RMFMKL.mm and gives all the fits in one output.

Value

A matrix showing the parameters of RS and FMKL generalised lambda distributions.

Note

RPRS can sometimes fail if it is not possible to calculate the percentiles of the data set. This usually happens when the number of data point is small.

References

Karian, Z. and E. Dudewicz (2000). Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalised Bootstrap Methods. New York, Chapman and Hall.

See Also

fun.RPRS.qs, fun.RMFMKL.qs, fun.data.fit.ml, fun.data.fit.hs, fun.data.fit.hs.nw , fun.data.fit.qs, fun.data.fit.lm

Examples

# Fitting normal(3,2) distriution using the default setting
 junk<-rnorm(50,3,2)
 fun.data.fit.mm(junk)

Description

This function fits generalised lambda distributions to data using quantile matching method

Usage

fun.data.fit.qs(data, rs.leap = 3, fmkl.leap = 3, rs.init = c(-1.5, 1.5), 
fmkl.init = c(-0.25, 1.5), FUN = "runif.sobol", trial.n = 100, len = 1000, 
type = 7, no = 10000)

Arguments

Details

This function consolidates fun.RPRS.qs and fun.RMFMKL.qs and gives all the fits in one output.

Value

A matrix showing the parameters of RS and FMKL generalised lambda distributions.

Note

RPRS can sometimes fail if it is not possible to calculate the percentiles of the data set. This usually happens when the number of data point is small.

Author(s)

Steve Su

References

Su (2008). Fitting GLD to data via quantile matching method. (Book chapter to appear)

See Also

fun.RPRS.qs, fun.RMFMKL.qs, fun.data.fit.ml, fun.data.fit.hs, fun.data.fit.hs.nw , fun.data.fit.mm, fun.data.fit.lm

Examples

# Fitting normal(3,2) distriution using the default setting
 junk<-rnorm(50,3,2)
 fun.data.fit.qs(junk)

Description

This function counts the number of times the p-value exceed 0.05 for the null hypothesis that the observations simulated from the fitted distribution is the same as the observations simulated from the unimodal data set.

Usage

fun.diag.ks.g(result, data, no.test = 1000, len = floor(0.9 * length(data)), 
param, alpha = 0.05)

Arguments

Value

A numerical value representing number of times the p-value exceeds alpha.

Note

If there are ties, jittering is used in ks.gof.

Author(s)

Steve Su

References

Stephens, M. A. (1986). Tests based on EDF statistics. In Goodness-of-Fit Techniques. D'Agostino, R. B. and Stevens, M. A., eds. New York: Marcel Dekker.

Su, S. (2005). A Discretized Approach to Flexibly Fit Generalized Lambda Distributions to Data. Journal of Modern Applied Statistical Methods (November): 408-424.

Su (2007). Nmerical Maximum Log Likelihood Estimation for Generalized Lambda Distributions. Computational Statistics and Data Analysis: *51*, 8, 3983-3998.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.diag.ks.g.bimodal

Examples

# Generate 1000 random observations from Normal distribution with mean=100, 
# standard deviation=10. Save this as junk
 junk<-rnorm(1000,100,10)

# Fit junk using RPRS method via the maxmum likelihood.
 fit1<-fun.RPRS.ml(junk, c(-1.5, 1.5), leap = 3)

# Calculate the simulated KS test result:
 fun.diag.ks.g(fit1,junk,param="rs")

Description

This function counts the number of times the p-value exceed 0.05 for the null hypothesis that the observations simulated from the fitted distribution is the same as the observations simulated from the bimodal data set.

Usage

fun.diag.ks.g.bimodal(result1, result2, prop1, prop2, data, no.test = 1000, 
len = floor(0.9 * length(data)), param1, param2, alpha = 0.05)

Arguments

Value

A numerical value representing number of times the p-value exceeds alpha.

Note

If there are ties, jittering is used in ks.gof.

Author(s)

Steve Su

References

Stephens, M. A. (1986). Tests based on EDF statistics. In Goodness- of-Fit Techniques. D'Agostino, R. B. and Stevens, M. A., eds. New York: Marcel Dekker.

Su, S. (2005). A Discretized Approach to Flexibly Fit Generalized Lambda Distributions to Data. Journal of Modern Applied Statistical Methods (November): 408-424.

Su (2007). Nmerical Maximum Log Likelihood Estimation for Generalized Lambda Distributions. Computational Statistics and Data Analysis: *51*, 8, 3983-3998.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.diag.ks.g

Examples

# Fit the faithful[,1] data from the MASS library
 fit1<-fun.auto.bimodal.ml(faithful[,1],init1.sel="rprs",init2.sel="rmfmkl",
 init1=c(-1.5,1,5),init2=c(-0.25,1.5),leap1=3,leap2=3)
# Run diagnostic KS tests
 fun.diag.ks.g.bimodal(fit1$par[1:4],fit1$par[5:8],prop1=fit1$par[9],
 data=faithful[,1],param1="rs",param2="fmkl")

Description

This function is primarily designed to be used for testing the fitted distribution with reference to a theoretical distribution. It is also tailored for output obtained from the fun.data.fit.ml function.

Usage

fun.diag1(result, test, no.test = 1000, alpha = 0.05)

Arguments

Value

A vector showing the number of times the KS p-value is greater than alpha for each of the distribution fit strategy.

Note

If there are ties, jittering is used in ks.gof.

Author(s)

Steve Su

References

Su, S. (2005). A Discretized Approach to Flexibly Fit Generalized Lambda Distributions to Data. Journal of Modern Applied Statistical Methods (November): 408-424.

Su, S. (2007). Numerical Maximum Log Likelihood Estimation for Generalized Lambda Distributions. Journal of Computational statistics and data analysis 51(8) 3983-3998.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.diag2, fun.diag.ks.g, fun.diag.ks.g.bimodal

Examples

# Fits a Weibull 5,2 distribution:
 weibull.approx.ml<-fun.data.fit.ml(rweibull(1000,5,2))

# Compute the resample K-S test results.
 fun.diag1(weibull.approx.ml, rweibull(100000, 5, 2))

Description

This function is primarily designed to be used for testing the fitted distribution with reference to an empirical data. It is also tailored for output obtained from the fun.data.fit.ml function.

Usage

fun.diag2(result, data, no.test = 1000, len=100, alpha = 0.05)

Arguments

Value

A vector showing the number of times the KS p-value is greater than alpha for each of the distribution fit strategy.

Note

If there are ties, jittering is used in ks.gof.

Author(s)

Steve Su

References

Su, S. (2005). A Discretized Approach to Flexibly Fit Generalized Lambda Distributions to Data. Journal of Modern Applied Statistical Methods (November): 408-424.

Su, S. (2007). Numerical Maximum Log Likelihood Estimation for Generalized Lambda Distributions. Journal of Computational statistics and data analysis 51(8) 3983-3998.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.diag1, fun.diag.ks.g, fun.diag.ks.g.bimodal

Examples

# Fits a Normal 3,2 distribution:
 junk<-rnorm(1000,3,2)
 fit<-fun.data.fit.ml(junk)

# Compute the resample K-S test results.
 fun.diag2(fit,junk)

Description

This function supplements fun.nclass.e and it is not intended to be used by the users directly.

Usage

fun.disc.estimation(x, nint)

Arguments

Details

The function cuts the vector into evenly spaced categories and estimate the mean and variance of the actual data based on the categorisation.

Value

Two numerical values, the first being the mean and the second being the variance.

Author(s)

Steve Su

See Also

fun.nclass.e

Examples

## Cut up a randomly normally distributed observations into 5 evenly spaced 
## categories and estimate the mean and variance based on this cateogorisation.
junk<-rnorm(1000,3,2)
fun.disc.estimation(junk,5)

Description

This function calls the runif.sobol, runif.sobol.owen and runif.halton essentially from the spacefillr package.

Usage

fun.gen.qrn(n, dimension, scrambling, FUN = "runif.sobol")

Arguments

Value

A vector of values if dimension=1, otherwise a matrix of values between 0 and 1.

Author(s)

Steve Su

Examples

fun.gen.qrn(1000,5,3,"runif.sobol")

fun.gen.qrn(1000,5,409,"QUnif")

Description

This function computes the first four L moments for both RS and FMKL generalised lambda distributions.

Usage

fun.lm.theo.gld(L1, L2, L3, L4, param)

Arguments

Value

A vector listing the first four L moments

Note

Sometimes the theoretical moments may not exist, in those cases, NA is returned.

Author(s)

Steve Su

References

Asquith, W. (2007). "L-moments and TL-moments of the generalized lambda distribution." Computational Statistics and Data Analysis 51(9): 4484-4496.

Karvanen, J. and A. Nuutinen (2008). "Characterizing the generalized lambda distribution by L-moments." Computational Statistics and Data Analysis 52(4): 1971-1983.

See Also

fun.theo.mv.gld

Examples

fun.lm.theo.gld(1, 2, 3, 4, "rs")
fun.lm.theo.gld(1, 2, 3, 4, "fmkl")

Description

This is a generic function that can be used to find mean, variance, sum or other operations according to some index imposed on the matrix or vector.

Usage

fun.mApply(X, INDEX, FUN = NULL, ..., simplify = TRUE)

Arguments

Value

If FUN returns more than one number, fun.mApply returns a matrix with rows corresponding to unique values of INDEX.

Author(s)

Tony Plate

Examples

# Finding the row medians of a matrix (matrix(1:20,nrow=5))
fun.mApply(matrix(1:20,nrow=5),list(1:5),median)

Description

This function checks the lowest and highest quantiles of the specified GLDs against the specified dataset

Usage

fun.minmax.check.gld(data, lambdas, param, lessequalmin = 1, 
greaterequalmax = 1)

Arguments

Details

lessequalmin==1 means the lowest value of GLD <= minimum value of data lessequalmin==0 means the lowest value of GLD < minimum value of data greaterequalmin==1 means the highest value of GLD >= maximum value of data greaterequalmin==0 means the highest value of GLD > maximum value of data

Value

A vector of logical values indicating whether the specified data the specified GLDs cover the minimum and the maximum values in a dataset

Author(s)

Steve Su

Examples

fun.minmax.check.gld(runif(100,.9,1),matrix(1:12,ncol=4),param="rs",0,0)
fun.minmax.check.gld(runif(100,.98,1),matrix(1:12,ncol=4),param="fkml",1,1)

Description

This functions compute the mean, variance, skewness and kurtosis of the fitted generalised lambda distribution mixtures using Monte Carlo simulation.

Usage

fun.moments.bimodal(result1, result2, prop1, prop2, len = 1000, 
no.test = 1000, param1, param2)

Arguments

Details

There is also a theoretical computation of the moments in fun.theo.bi.mv.gld, it should be noted that the theoretical moments may not exist. The length of object in len means how many observations should be generated in each simulation run, with the number of simulation runs governed by no.test.

Value

A matrix with four columns showing the mean, variance, skewness and kurtosis of the fitted generalised lambda distribution mixtures using Monte Carlo simulation. Each row represents a simulation run.

Author(s)

Steve Su

See Also

fun.theo.bi.mv.gld, fun.simu.bimodal, fun.rawmoments

Examples

# Fitting the first column of the Old Faithful Geyser data
 fit1<-fun.auto.bimodal.ml(faithful[,1],init1.sel="rmfmkl",init2.sel="rmfmkl",
 init1=c(-0.25,1.5),init2=c(-0.25,1.5),leap1=3,leap2=3)

# After fitting compute the monte carlo moments using fun.moments.bimodal
 fun.moments.bimodal(fit1$par[1:4],fit1$par[5:8],prop1=fit1$par[9],
 param1="fmkl",param2="fmkl")

# It is also possible to compare this with the moments of the original dataset:
 fun.moments(faithful[,1])

Description

This function evaluates the mean, variance, skewness and kurtosis of a numerical vector. Missing values are automatically removed.

Usage

fun.moments.r(x, normalise = "N")

Arguments

Value

A vector of mean, variance, skewness and kurtosis.

Note

Please contact the author directly if you find a bug!

Author(s)

Steve Su

See Also

fun.theo.mv.gld

Examples

fun.moments.r(rnorm(1000))
fun.moments.r(rnorm(1000),normalise="Y")

Description

Support function for discretised method of fitting distribution to data.

Usage

fun.nclass.e(x)

Arguments

Details

This function calculates the mean and variance of the discretised data from 1 to the very last observation and chooses the best number of categories that represent the mean and variance of the actual data set through the criterion of squared deviations.

Value

A numerical value suggesting the best number of class that can be used to represent the mean and variane of the original data set.

Note

This is not designed to be called directly by end user.

Author(s)

Steve Su

See Also

fun.disc.estimation

Examples

fun.nclass.e(rnorm(100,3,2))

Description

This function is designed for univariate generalised lambda distribution fits only.

Usage

fun.plot.fit(fit.obj, data, nclass = 50, xlab = "", name = "", param.vec,
ylab="Density", main="")

Arguments

Value

A graphical output showing the data and the resulting distributional fits.

Note

If the distribution fits over fits the peak of the distribution, it can be difficult to see the actual data set.

Author(s)

Steve Su

See Also

fun.plot.fit.bm, fun.data.fit.ml, fun.data.fit.hs, fun.data.fit.hs.nw, fun.RPRS.ml, fun.RMFMKL.ml, fun.RPRS.hs, fun.RMFMKL.hs, fun.RPRS.hs.nw, fun.RMFMKL.hs.nw

Examples

# Generate Normally distribute random numbers as dataset
 junk<-rnorm(1000,3,2)

# Fit the data set using fun.data.fit.ml. 
# Also, fun.data.fit.hs or fun.data.fit.hs.nw can be used.
 obj.fit<-fun.data.fit.ml(junk)

# Plot the resulting fits
 fun.plot.fit(obj.fit,junk,xlab="x",name=".ML",param.vec=c("rs","fmkl","fmkl"))

# This function also works for singular fits such as those by fun.RPRS.ml,
# fun.RMFMKL.ml, fun.RPRS.hs, fun.RMFMKL.hs, fun.RPRS.hs.nw, fun.RMFMKL.hs.nw
 junk<-rnorm(1000,3,2)
 obj.fit<-fun.RPRS.ml(junk)
 fun.plot.fit(obj.fit,junk,xlab="x",name="RPRS.ML",param.vec=c("rs"))

Description

This function is designed for mixture of two generalised lambda distributions only.

Usage

fun.plot.fit.bm(fit.obj, data, nclass = 50, xlab = "", name = "", main="", 
param.vec, ylab="Density")

Arguments

Value

A graphical output showing the data and the resulting distributional fits.

Note

If the distribution fits over fits the peak of the distribution, it can be difficult to see the actual data set.

Author(s)

Steve Su

See Also

fun.auto.bimodal.ml, fun.auto.bimodal.pml, fun.plot.fit

Examples

opar <- par() 
 par(mfrow=c(2,1))

# Fitting mixture of generalised lambda distributions on the data set using 
# both the maximum likelihood and partition maximum likelihood and plot 
# the resulting fits

 junk<-fun.auto.bimodal.ml(faithful[,1],per.of.mix=0.1,clustering.m=clara,
 init1.sel="rprs",init2.sel="rmfmkl",init1=c(-1.5,1,5),init2=c(-0.25,1.5),
 leap1=3,leap2=3)
 fun.plot.fit.bm(nclass=50,fit.obj=junk,data=faithful[,1],
 name="Maximum likelihood using",xlab="faithful1",param.vec=c("rs","fmkl"))

 junk<-fun.auto.bimodal.pml(faithful[,1],clustering.m=clara,init1.sel="rprs",
 init2.sel="rmfmkl",init1=c(-1.5,1,5),init2=c(-0.25,1.5),leap1=3,leap2=3)
 fun.plot.fit.bm(nclass=50,fit.obj=junk,data=faithful[,1],
 name="Partition maximum likelihood using",xlab="faithful1",
 param.vec=c("rs","fmkl"))

 junk<-fun.auto.bimodal.ml(faithful[,1],per.of.mix=0.1,clustering.m=clara,
 init1.sel="rprs",init2.sel="rmfmkl",init1=c(-1.5,1,5),init2=c(-0.25,1.5),
 leap1=3,leap2=3)
 fun.plot.fit.bm(nclass=50,fit.obj=junk,data=faithful[,1],
 main="Mixture distribution fit",
 name="RS and FMKL GLD",xlab="faithful1",param.vec=c("rs","fmkl"))

 par(opar)

Description

This is a variant of the fun.plot.fit function.

Usage

fun.plot.many.gld(fit.obj, data, xlab="", ylab="Density", main="", legd="",
param.vec)

Arguments

Value

A graph showing the different distributions on the same page.

Note

The data part of the function is not plotted, to see the dataset use the fun.plot.fit function.

Author(s)

Steve Su

See Also

fun.plot.fit, fun.plot.fit.bm

Examples

# Fit the dataset
 junk<-rnorm(1000,3,2)
 result.hs<-fun.data.fit.hs(junk,rs.default = "Y", fmkl.default = "Y", 
 rs.leap=3, fmkl.leap=3,rs.init = c(-1.5, 1.5), fmkl.init = c(-0.25, 1.5),
 no.c.rs=50,no.c.fmkl=50)

 opar <- par() 
 par(mfrow=c(2,2))

# Plot the entire data range
 fun.plot.many.gld(result.hs,junk,"x","density","",
 legd=c("RPRS.hs", "RMFMKL.hs"))

# Plot and compare parts of the distributions
 fun.plot.many.gld(result.hs,c(1,2),"x","density","",legd=c("RPRS.hs", 
"RMFMKL.hs"))
 fun.plot.many.gld(result.hs,c(0.1,0,2),"x","density","",legd=c("RPRS.hs", 
"RMFMKL.hs"))
 fun.plot.many.gld(result.hs,c(3,4),"x","density","",legd=c("RPRS.hs", 
"RMFMKL.hs"))

 par(opar)

Description

This function is of theoretical interest only.

Usage

fun.rawmoments(L1, L2, L3, L4, param = "fmkl")

Arguments

Details

This function is the building block for fun.theo.bi.mv.gld.

Value

A vector showing the raw moments of the specified generalised lambda distribution up to the fourth order.

Author(s)

Steve Su

References

Freimer, M., Mudholkar, G. S., Kollia, G. & Lin, C. T. (1988), A study of the generalized tukey lambda family, Communications in Statistics - Theory and Methods *17*, 3547-3567.

Karian, Zaven A. and Dudewicz, Edward J. (2000), Fitting statistical distributions: the Generalized Lambda Distribution and Generalized Bootstrap methods, Chapman & Hall

Ramberg, J. S. & Schmeiser, B. W. (1974), An approximate method for generating asymmetric random variables, Communications of the ACM *17*, 78-82.

See Also

~~objects to See Also as help, ~~~

Examples

## Generate some random numbers using FMKL and RS generalised lambda 
## distributions and then compute the empirical and theoretical 
## E(X), E(X^2), E(X^3), E(X^4) 

junk<-rgl(100000,1,2,3,4)
mean(junk)
mean(junk^2)
mean(junk^3)
mean(junk^4)

junk<-rgl(100000,1,2,3,4,"rs")
mean(junk)
mean(junk^2)
mean(junk^3)
mean(junk^4)

fun.rawmoments(1,2,3,4)
fun.rawmoments(1,2,3,4,"rs")

Description

This function fits FMKL generalised distribution to data using discretised approach with weights. It is designed to act as a smoother device rather than as a definitive fit.

Usage

fun.RMFMKL.hs(data, default = "Y", fmkl.init = c(-0.25, 1.5), no.c.fmkl = 50, 
leap = 3,FUN="runif.sobol",no=10000)

Arguments

Details

This function optimises the deviations of frequency of the bins to that of the theoretical so it has the effect of "fitting clothes" onto the data set. The user can decide the frequency of the bins they want the distribution to smooth over. The resulting fit may or may not be an adequate fit from a formal statistical point of view such as satisfying the goodness of fit for example, but it can be useful to suggest the range of different distributions exhibited by the data set. The default number of classes calculates the mean and variance after categorising the data into different bins and uses the number of classes that best matches the mean and variance of the original, ungrouped data. The weighting is designed to accentuate the peak or the dense part of the distribution and suppress the tails.

Value

A vector representing four parametefmkl of the FMKL generalised lambda distribution.

Note

In some cases, the resulting fit may not converge, there are currently no checking mechanism in place to ensure global convergence.

Author(s)

Steve Su

References

Su, S. (2005). A Discretized Approach to Flexibly Fit Generalized Lambda Distributions to Data. Journal of Modern Applied Statistical Methods (November): 408-424.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.RMFMKL.hs.nw, fun.RPRS.hs.nw, fun.RPRS.hs, fun.data.fit.hs, fun.data.fit.hs.nw

Examples

# Using the default number of classes
 fun.RMFMKL.hs(data=rnorm(1000,3,2),default="Y",fmkl.init=c(-0.25,1.5),leap=3)
# Using 20 classes
 fun.RMFMKL.hs(data=rnorm(1000,3,2),default="N",fmkl.init=c(-0.25,1.5),
 no.c.fmkl=20,leap=3)

Description

This function fits FMKL generalised distribution to data using discretised approach without weights. It is designed to act as a smoother device rather than as a definitive fit.

Usage

fun.RMFMKL.hs.nw(data, default = "Y", fmkl.init = c(-0.25, 1.5), 
no.c.fmkl = 50, leap = 3,FUN="runif.sobol",no=10000)

Arguments

Details

This function optimises the deviations of frequency of the bins to that of the theoretical so it has the effect of "fitting clothes" onto the data set. The user can decide the frequency of the bins they want the distribution to smooth over. The resulting fit may or may not be an adequate fit from a formal statistical point of view such as satisfying the goodness of fit for example, but it can be useful to suggest the range of different distributions exhibited by the data set. The default number of classes calculates the mean and variance after categorising the data into different bins and uses the number of classes that best matches the mean and variance of the original, ungrouped data.

Value

A vector representing four parameters of the FMKL generalised lambda distribution.

Note

In some cases, the resulting fit may not converge, there are currently no checking mechanism in place to ensure global convergence.

Author(s)

Steve Su

References

Su, S. (2005). A Discretized Approach to Flexibly Fit Generalized Lambda Distributions to Data. Journal of Modern Applied Statistical Methods (November): 408-424.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.RPRS.hs.nw, fun.RMFMKL.hs, fun.RPRS.hs, fun.data.fit.hs, fun.data.fit.hs.nw

Examples

# Using the default number of classes
 fun.RMFMKL.hs.nw(data=rnorm(1000,3,2),default="Y",
 fmkl.init=c(-0.25,1.5),leap=3)
# Using 20 classes
 fun.RMFMKL.hs.nw(data=rnorm(1000,6,5),default="N",fmkl.init=c(-0.25,1.5),
 no.c.fmkl=20,leap=3)

Description

This function fits FMKL generalised lambda distribution to data set using L moment matching

Usage

fun.RMFMKL.lm(data, fmkl.init = c(-0.25, 1.5), leap = 3, FUN = "runif.sobol", 
no = 10000)

Arguments

Details

This function provides method of L moment fitting scheme for FMKL GLD. Note this function can fail if there are no defined percentiles from the data set or if the initial values do not lead to a valid FMKL generalised lambda distribution.

This function is based on scheme detailed in the literature below but it has been modified by the author (Steve Su).

Value

A vector representing four parametefmkl of the FMKL generalised lambda distribution.

Author(s)

Steve Su

References

Asquith, W. (2007). "L-moments and TL-moments of the generalized lambda distribution." Computational Statistics and Data Analysis 51(9): 4484-4496.

Karvanen, J. and A. Nuutinen (2008). "Characterizing the generalized lambda distribution by L-moments." Computational Statistics and Data Analysis 52(4): 1971-1983.

See Also

fun.RMFMKL.ml, fun.RMFMKL.mm, fun.RMFMKL.qs, fun.data.fit.ml fun.data.fit.lm, fun.data.fit.qs, fun.data.fit.mm

Examples

# Fitting the normal distribution
 fun.RMFMKL.lm(data=rnorm(1000,2,3),fmkl.init=c(-0.25,1.5),leap=3)

Description

This function fits FMKL generalised lambda distribution to data set using maximum likelihood estimation.

Usage

fun.RMFMKL.ml(data, fmkl.init = c(-0.25, 1.5), leap = 3,FUN="runif.sobol",
no=10000)

Arguments

Details

This function provides one of the definitive fit to data set using generalised lambda distributions.

Value

A vector representing four parameters of the FMKL generalised lambda distribution.

Author(s)

Steve Su

References

Su, S. (2007). Numerical Maximum Log Likelihood Estimation for Generalized Lambda Distributions. Journal of Computational statistics and data analysis 51(8) 3983-3998.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.RPRS.ml, fun.data.fit.ml, fun.data.fit.qs

Examples

# Fitting the normal distribution
 fun.RMFMKL.ml(data=rnorm(1000,2,3),fmkl.init=c(-0.25,1.5),leap=3)

Description

This function fits FMKL generalised lambda distribution to data set using maximum likelihood estimation using faster implementation through C programming

Usage

fun.RMFMKL.ml.m(data, fmkl.init = c(-0.25, 1.5), leap = 3, FUN = "runif.sobol", 
no = 10000)

Arguments

Details

This function provides one of the definitive fit to data set using generalised lambda distributions.

Value

A vector representing four parameters of the FMKL generalised lambda distribution.

Author(s)

Steve Su

References

Su, S. (2007). Numerical Maximum Log Likelihood Estimation for Generalized Lambda Distributions. Journal of Computational statistics and data analysis 51(8) 3983-3998.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.RMFMKL.ml

Examples

# Fitting the normal distribution
 fun.RMFMKL.ml.m(data=rnorm(1000,2,3),fmkl.init=c(-0.25,1.5),leap=3)

Description

This function fits FMKL generalised lambda distribution to data set using moment matching

Usage

fun.RMFMKL.mm(data, fmkl.init = c(-0.25, 1.5), leap = 3, FUN = "runif.sobol", 
no = 10000)

Arguments

Details

This function provides method of moment fitting scheme for FMKL GLD. Note this function can fail if there are no defined percentiles from the data set or if the initial values do not lead to a valid FMKL generalised lambda distribution.

This function is based on scheme detailed in the literature below but it has been modified by the author (Steve Su).

Value

A vector representing four parametefmkl of the FMKL generalised lambda distribution.

Author(s)

Steve Su

References

Karian, Z. and E. Dudewicz (2000). Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalised Bootstrap Methods. New York, Chapman and Hall.

See Also

fun.RMFMKL.ml, fun.RMFMKL.lm, fun.RMFMKL.qs, fun.data.fit.ml fun.data.fit.lm, fun.data.fit.qs, fun.data.fit.mm

Examples

# Fitting the normal distribution
 fun.RMFMKL.mm(data=rnorm(1000,2,3),fmkl.init=c(-0.25,1.5),leap=3)

Description

This function fits FMKL generalised lambda distribution to data set using quantile matching

Usage

fun.RMFMKL.qs(data, fmkl.init = c(-0.25, 1.5), leap = 3, FUN = "runif.sobol", 
trial.n = 100, len = 1000, type = 7, no = 10000)

Arguments

Details

This function provides quantile matching fitting scheme for FMKL GLD. Note this function can fail if there are no defined percentiles from the data set or if the initial values do not lead to a valid FMKL generalised lambda distribution.

Value

A vector representing four parametefmkl of the FMKL generalised lambda distribution.

Author(s)

Steve Su

References

Su (2008). Fitting GLD to data via quantile matching method. (Book chapter to appear)

See Also

fun.RMFMKL.ml, fun.RMFMKL.lm, fun.RMFMKL.mm, fun.data.fit.ml fun.data.fit.lm, fun.data.fit.qs, fun.data.fit.mm

Examples

# Fitting the normal distribution
 fun.RMFMKL.qs(data=rnorm(1000,2,3),fmkl.init=c(-0.25,1.5),leap=3)

Description

This function fits RS generalised distribution to data using discretised approach with weights. It is designed to act as a smoother device rather than as a definitive fit.

Usage

fun.RPRS.hs(data, default = "Y", rs.init = c(-1.5, 1.5), no.c.rs = 50, 
leap = 3,FUN="runif.sobol",no=10000)

Arguments

Details

This function optimises the deviations of frequency of the bins to that of the theoretical so it has the effect of "fitting clothes" onto the data set. The user can decide the frequency of the bins they want the distribution to smooth over. The resulting fit may or may not be an adequate fit from a formal statistical point of view such as satisfying the goodness of fit for example, but it can be useful to suggest the range of different distributions exhibited by the data set. The default number of classes calculates the mean and variance after categorising the data into different bins and uses the number of classes that best matches the mean and variance of the original, ungrouped data. The weighting is designed to accentuate the peak or the dense part of the distribution and suppress the tails.

Value

A vector representing four parameters of the RS generalised lambda distribution.

Note

In some cases, the resulting fit may not converge, there are currently no checking mechanism in place to ensure global convergence. The RPRS method can sometimes fail if there are no valid percentiles in the data set or if initial values do not give a valid distribution.

Author(s)

Steve Su

References

Su, S. (2005). A Discretized Approach to Flexibly Fit Generalized Lambda Distributions to Data. Journal of Modern Applied Statistical Methods (November): 408-424.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.RPRS.hs.nw, fun.RMFMKL.hs.nw, fun.RMFMKL.hs, fun.data.fit.hs, fun.data.fit.hs.nw

Examples

# Using the default number of classes
 fun.RPRS.hs(data=rnorm(1000,2,3),default="Y",rs.init=c(-1.5,1.5),leap=3)
# Using 20 classes
 fun.RPRS.hs(data=rnorm(1000,2,3),default="N",rs.init=c(-1.5,1.5),
 no.c.rs=20,leap=3)

Description

This function fits RS generalised distribution to data using discretised approach without weights. It is designed to act as a smoother device rather than as a definitive fit.

Usage

fun.RPRS.hs.nw(data, default = "Y", rs.init = c(-1.5, 1.5), no.c.rs = 50, 
leap = 3,FUN="runif.sobol",no=10000)

Arguments

Details

This function optimises the deviations of frequency of the bins to that of the theoretical so it has the effect of "fitting clothes" onto the data set. The user can decide the frequency of the bins they want the distribution to smooth over. The resulting fit may or may not be an adequate fit from a formal statistical point of view such as satisfying the goodness of fit for example, but it can be useful to suggest the range of different distributions exhibited by the data set. The default number of classes calculates the mean and variance after categorising the data into different bins and uses the number of classes that best matches the mean and variance of the original, ungrouped data.

Value

A vector representing four parameters of the RS generalised lambda distribution.

Note

In some cases, the resulting fit may not converge, there are currently no checking mechanism in place to ensure global convergence. The RPRS method can sometimes fail if there are no valid percentiles in the data set or if initial values do not give a valid distribution.

Author(s)

Steve Su

References

Su, S. (2005). A Discretized Approach to Flexibly Fit Generalized Lambda Distributions to Data. Journal of Modern Applied Statistical Methods (November): 408-424.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.RPRS.hs.nw, fun.RPRS.hs, fun.RMFMKL.hs, fun.data.fit.hs, fun.data.fit.hs.nw

Examples

# Using the default number of classes
 fun.RPRS.hs.nw(data=rnorm(1000,3,2),default="Y",rs.init=c(-1.5,1.5),leap=3)
# Using 20 classes
 fun.RPRS.hs.nw(data=rnorm(1000,3,2),default="N",rs.init=c(-1.5,1.5),
 no.c.rs=20,leap=3)

Description

This function fits RS generalised lambda distribution to data set using L moment matching

Usage

fun.RPRS.lm(data, rs.init = c(-1.5, 1.5), leap = 3, FUN = "runif.sobol", 
no = 10000)

Arguments

Details

This function provides method of L moment fitting scheme for RS GLD. Note this function can fail if there are no defined percentiles from the data set or if the initial values do not lead to a valid RS generalised lambda distribution.

This function is based on scheme detailed in the literature below but it has been modified by the author (Steve Su).

Value

A vector representing four parameters of the RS generalised lambda distribution.

Author(s)

Steve Su

References

Asquith, W. (2007). "L-moments and TL-moments of the generalized lambda distribution." Computational Statistics and Data Analysis 51(9): 4484-4496.

Karvanen, J. and A. Nuutinen (2008). "Characterizing the generalized lambda distribution by L-moments." Computational Statistics and Data Analysis 52(4): 1971-1983.

See Also

fun.RPRS.ml, fun.RPRS.mm, fun.RPRS.qs, fun.data.fit.ml fun.data.fit.lm, fun.data.fit.qs, fun.data.fit.mm

Examples

# Fitting the normal distribution
 fun.RPRS.lm(data=rnorm(1000,2,3),rs.init=c(-1.5,1.5),leap=3)

Description

This function fits RS generalised lambda distribution to data set using maximum likelihood estimation.

Usage

fun.RPRS.ml(data, rs.init = c(-1.5, 1.5), leap = 3,FUN="runif.sobol",no=10000)

Arguments

Details

This function provides one of the definitive fit to data set using generalised lambda distributions. Note this function can fail if there are no defined percentiles from the data set or if the initial values do not lead to a valid RS generalised lambda distribution.

Value

A vector representing four parameters of the RS generalised lambda distribution.

Author(s)

Steve Su

References

Su, S. (2007). Numerical Maximum Log Likelihood Estimation for Generalized Lambda Distributions. Computational statistics and data analysis 51(8) 3983-3998.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.RMFMKL.ml, fun.data.fit.ml, fun.data.fit.qs

Examples

# Fitting the normal distribution
 fun.RPRS.ml(data=rnorm(1000,2,3),rs.init=c(-1.5,1.5),leap=3)

Description

This function fits RS generalised lambda distribution to data set using maximum likelihood estimation using faster implementation through C programming

Usage

fun.RPRS.ml.m(data, rs.init = c(-1.5, 1.5), leap = 3, FUN = "runif.sobol", 
no = 10000)

Arguments

Details

This function provides one of the definitive fit to data set using generalised lambda distributions. Note this function can fail if there are no defined percentiles from the data set or if the initial values do not lead to a valid RS generalised lambda distribution.

Value

A vector representing four parameters of the RS generalised lambda distribution.

Author(s)

Steve Su

References

Su, S. (2007). Numerical Maximum Log Likelihood Estimation for Generalized Lambda Distributions. Computational statistics and data analysis 51(8) 3983-3998.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.RPRS.ml

Examples

# Fitting the normal distribution
 fun.RPRS.ml.m(data=rnorm(1000,2,3),rs.init=c(-1.5,1.5),leap=3)

Description

This function fits RS generalised lambda distribution to data set using moment matching

Usage

fun.RPRS.mm(data, rs.init = c(-1.5, 1.5), leap = 3, FUN = "runif.sobol", 
no = 10000)

Arguments

Details

This function provides method of moment fitting scheme for RS GLD. Note this function can fail if there are no defined percentiles from the data set or if the initial values do not lead to a valid RS generalised lambda distribution.

This function is based on scheme detailed in the literature below but it has been modified by the author (Steve Su).

Value

A vector representing four parameters of the RS generalised lambda distribution.

Author(s)

Steve Su

References

Karian, Z. and E. Dudewicz (2000). Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalised Bootstrap Methods. New York, Chapman and Hall.

See Also

fun.RPRS.ml, fun.RPRS.lm, fun.RPRS.qs, fun.data.fit.ml fun.data.fit.lm, fun.data.fit.qs, fun.data.fit.mm