The hardware and bandwidth for this mirror is donated by dogado GmbH, the Webhosting and Full Service-Cloud Provider. Check out our Wordpress Tutorial.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]dogado.de.

Version: 2.3.3
Date: 2018-3-31
Title: Generalize Lambda Distribution and Generalized Bootstrapping
Author: Bin Wang <bwang@southalabama.edu>.
Maintainer: Bin Wang <bwang@southalabama.edu>
Depends: R (≥ 2.5.0), boot, KernSmooth
Description: A collection of algorithms and functions for fitting data to a generalized lambda distribution via moment matching methods, and generalized bootstrapping.
License: Unlimited
Packaged: 2018-04-01 15:02:11 UTC; bwang
Repository: CRAN
Date/Publication: 2018-04-01 16:49:51 UTC
NeedsCompilation: yes

Compute Average Run Length

Description

Compute average run length for control chart.

Usage

 ARL1(x,K,pm1,pI1)
 ARL0(x,ARL0=370,gridsize=20)

Arguments

x

An R object generate using kde function from package ks.

K

a vector of the levels

ARL0

in-control average run length

pm1, pI1

out-of-control parameters for the control chart.

gridsize

Gridsize of countour levels to search for ARL.

Author(s)

B. Wang bwang@southalabama.edu

References

Yang, S.F. and Wang, B. “Using A Kernel Control Region to Monitor Both the Process Location and Dispersion”.


Basic functions for RS-GLD

Description

To compute the density, distribution, quantile, and to generate random sample for RS-GLD.

Usage

## Default S3 method:
degld(x,lambda)
pegld(x,lambda)
qegld(p,lambda)
regld(n,lambda)

Arguments

x

a numeric value or a vector.

p

a probability or a vector of probabilities.

n

sample size.

lambda

a vector of four parameters for RS-GLD.

Author(s)

B. Wang bwang@jaguar1.usouthal.edu

References

Karian, Z.A., Dudewicz, E.J., 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, Comm. in Statist.- Simul. \& Comput. 25(3), 611-642.

Karian, Z.A., Dudewicz, E.J., 2000. Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalized Bootstrap Methods, Chapman and Hall/CRC.

See Also

fit.egld, qrsgld,prsgld, rrsgld,drsgld.

Examples


lambdas = c(2,4,3,4)
shape=3;scale=4
x0 = rbeta(5,shape,scale)
x1 = x0*lambdas[2]+lambdas[1]
qegld(c(0,.1,.5,.7,1),lambdas)
qbeta(c(0,.1,.5,.7,1),shape,scale)*lambdas[2]+lambdas[1]

pegld(x1,lambdas)
pbeta(x0,shape,scale)

degld(x1,lambdas)
dbeta(x0,shape,scale)/lambdas[2]

x0 = sort(rbeta(1000,shape,scale))
y = x0*lambdas[2]+lambdas[1]
plot(dbeta(x0,shape,scale)/lambdas[2]~y,type='l')
lines(degld(y,lambdas)~y,lty=2,col=2)
lines(density(y),col=4,lty=3)


Basic functions for RS-GLD

Description

To compute the density, distribution, quantile, and to generate random sample for RS-GLD.

Usage

## Default S3 method:
drsgld(x,lambda)
prsgld(x,lambda)
qrsgld(p,lambda)
rrsgld(n,lambda)

Arguments

x

a numeric value or a vector.

p

a probability or a vector of probabilities.

n

sample size.

lambda

a vector of four parameters for RS-GLD.

Author(s)

B. Wang bwang@jaguar1.usouthal.edu

References

Karian, Z.A., Dudewicz, E.J., 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, Comm. in Statist.- Simul. \& Comput. 25(3), 611-642.

Karian, Z.A., Dudewicz, E.J., 2000. Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalized Bootstrap Methods, Chapman and Hall/CRC.

See Also

fit.gld, qegld,pegld, regld,degld.

Examples


lambdas = c(0, 0.1975, 0.1349,0.1349)
qrsgld(c(0,.1,.5,.7,1),lambdas)
prsgld(c(-10,0,1,3,20),lambdas)
drsgld(c(-10,0,1,3,20),lambdas)
x = sort(rrsgld(100,lambdas))
plot(dnorm(x)~x,type='l')
lines(drsgld(x,lambdas)~x,lty=2,col=2)
lines(density(x),col=4,lty=3)


Fit Extended Generalized Lambda Distribution (EGLD/GBD)

Description

To fit a EGLD or generalize beta distribution with the maximum likelihood methods.

Usage

  fit.egld(x,xmin=NULL,xmax=NULL)

Arguments

x

A sample. 'NA' values will be automatically removed.

xmin

The lower limit of the underlying distribution. Default: NULL.

xmax

The upper limit of the underlying distribution. Default: NULL.

Author(s)

B. Wang bwang@jaguar1.usouthal.edu

References

Karian, Z.A., Dudewicz, E.J., 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, Comm. in Statist.- Simul. \& Comput. 25(3), 611-642.

Karian, Z.A., Dudewicz, E.J., 2000. Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalized Bootstrap Methods, Chapman and Hall/CRC.

See Also

fit.gld, qrsgld,prsgld, rrsgld,drsgld.

Examples


b3=4;b4=4; b1=1;b2=5; # EGLD(b1,b2,b3,b4)
b1=0;b2=1; # equivalently beta(b3,b4)
b1=-3;b2=5; 
xr = rbeta(100,b3,b4)
x = xr * b2 + b1 
min(x); range(x)
sum(dbeta(xr,b3,b4,1))
x0 = seq(min(x),max(x),length=100)
x1 = (x0-b1)/b2
plot(dbeta(x1,b3,b4)/b2~x0,type='l',lwd=2,col=2)
lines(density(x),lty=2, col=2)

## no prior information on min and max
(out0 = fit.egld(x))
lines(out0,col=1)
## xmin known
(out1 = fit.egld(x,xmin=-3))
lines(out1,col=3,lwd=2)
## xmax known
(out2 = fit.egld(x,xmax=2))
lines(out2, col=4)
## both known
(out3 = fit.egld(x,xmin=-3,xmax=2))
lines(out3, col=5)



Fitting a Ramberg-Schmeiser-Tukey (RST) lambda distribution

Description

To fit a Ramberg-Schmeiser-Tukey (RST) lambda distribution with the three moment-matching methods.

Usage

  fit.gld(x,method='LMoM')

Arguments

x

A sample of size at least 6. 'NA' values will be automatically removed.

method

Choose GLD fitting method. Default: 'LMoM'. Other options: 'MoM'– method of moments; "MoP", method of percentiles; "LMoM", method of L-moments. 'best' chooses the best fit from the above three methods, which takes a while.

Author(s)

B. Wang bwang@jaguar1.usouthal.edu

References

Karian, Z.A., Dudewicz, E.J., 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, Comm. in Statist.- Simul. \& Comput. 25(3), 611-642.

Karian, Z.A., Dudewicz, E.J., 2000. Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalized Bootstrap Methods, Chapman and Hall/CRC.

See Also

fit.egld, qrsgld,prsgld, rrsgld,drsgld.

Examples


mu = 34.5; sig=1.5
y = rnorm(1000,mu,sig)
x = round(y)  ###  rounding errors

x0 = seq(min(y),max(y),length=100)
f0 = dnorm(x0,mu,sig)
plot(f0~x0,type='l')
lines(density(y),col=4)
## fit with method of moments
(out1 = fit.gld(x, method='MoM')) 
lines(out1,col=2)
##  Method of percentile
(out2 = fit.gld(x, method='mop'))
lines(out2, col=3)
## Method of L-moments
(out3 = fit.gld(x, method='lmom'))
lines(out3, col=5)
##  Fitting EGLD
(out0 = fit.egld(x))
lines(out0,col=6)

legend(max(x0), max(f0), xjust=1,yjust=1,
  legend=c("true","kde","MoM","MoP","LMoM","egld"),
  lty=c(1,1,1,1,1,1),
  col=c(1,4,2,3,5,6))


Estimate Asymptotic Joint Distribution of EWMA variables

Description

Estimate Asymptotic Joint Distribution of EWMA variables for control chart.

Usage

  fkde(n=5, pm0=0.5, pI0=0.2, lambda=0.05,
       gridsize=100,B=10000,T=10000)

Arguments

n

sample size.

lambda

a parameter to compute EWMA

pm0, pI0

in-control parameters for the control chart.

gridsize

gridsize to evalue the joint PDF values

B, T

iteration times and maximum time of t to generate random samples for density estimation

Author(s)

B. Wang bwang@southalabama.edu

References

Yang, S.F. and Wang, B. “Using A Kernel Control Region to Monitor Both the Process Location and Dispersion”.


Generalized bootstrapping

Description

Generalized bootstrapping

Usage

  gboot(x,gldobj,statistic,...)

Arguments

x

A random sample.

gldobj

Either an object fitting a GLD or EGLD to data 'x'.

statistic

User defined function to resample from 'x'. 'fun' could be parametric or non-parametric.

...

Controls

References

Wang, B., Mishra, S.N., Mulekar, M., Mishra, N.S., Huang, K., (2010). Generalized Bootstrap Confidence Intervals for High Quantiles, In: Karian ZA, Dudewicz, EJ eds. The Handbook on Fitting Statistical Distributions with R. CRC Press. 2010: 877-913.

Wang, B., Mishra, S.N., Mulekar, M., Mishra, N.S., Huang, K., (2010). Comparison of bootstrap and generalized bootstrap methods for estimating high quantiles, Journal of Statistical Planning and Inferences, 140. 2926-2935. DOI: 10.1016/j.jspi.2010.03.016.

Karian, Z.A., Dudewicz, E.J., 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, Comm. in Statist.- Simul. \& Comput. 25(3), 611-642.

Karian, Z.A., Dudewicz, E.J., 2000. Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalized Bootstrap Methods, Chapman and Hall/CRC.

Dudewicz, E.J., 1992. The Generalized Bootstrap, Bootstrapping and Related Techniques, In: K.H., G. Rothe, W. Sendler, eds., V. 376 of Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, 31-37.

Examples


data(ofc)
X = ofc$x0
Ta = function(x) mean(x<31)
gld0 = fit.gld(X)
(out = gboot(X,gld0,statistic=Ta,R=100))
gld1 = fit.egld(X)
(out = gboot(X,gld1,statistic=Ta,R=100))


OFC data

Description

Simulated head size data of new borns.

Usage

data(ofc)

Format

A data frame with 1000 observations on 2 variables.

x0 numeric Original OFC values
x numeric OFC values rounded to centimeters

References

Wang, CSDA and JSS papers.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.