Log-Pearson Type III Distribution

Description

Density, distribution function, quantile function and random generation for the log-Pearson type III distribution with shape1, shape2, and scale parameters equal to shape, scale, and thres, respectively.

Usage

dlgamma3(x,shape=1,scale=1,thres=1,log=FALSE)
plgamma3(q,shape=1,scale=1,thres=1,lower.tail=TRUE,log.p=FALSE)
qlgamma3(p,shape=1,scale=1,thres=1,lower.tail=TRUE,log.p=FALSE)
rlgamma3(n,shape=1,scale=1,thres=1)

Arguments

Details

If Y is a random variable distributed according to a gamma distribution (with shape and scale parameters), then X = exp(Y+m) has a log-Pearson type III distribution with shape1 and shape2 parameters corresponding to the shape and 1/scale parameteres of Y, and with scale parameter m.

Value

dlgamma3 gives the density, plgamma3 gives the distribution function, qlgamma3 gives the quantile function, and rlgamma3 generates random deviates.

References

BOBEE, B. and F. ASHKAR (1991). The Gamma Family and Derived Distributions Applied in Hydrology. Water Resources Publications, Littleton, Colo., 217 p.

See Also

dgamma, pgamma, qgamma, rgamma, dgamma3, pgamma3, qgamma3, rgamma3

Examples

thres <- 10
x <- rlgamma3(n=10,shape=2,scale=11,thres=thres)
dlgamma3(x,2,11,thres)
dgamma3(log(x),2,1/11,thres)/x
dgamma(log(x)-thres,2,11)/x

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(FAdist)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/FAdist/LGAMMA3.Rd_%03d_medium.png", width=480, height=480)
> ### Name: LGAMMA3
> ### Title: Log-Pearson Type III Distribution
> ### Aliases: dlgamma3 plgamma3 qlgamma3 rlgamma3
> ### Keywords: distribution
> 
> ### ** Examples
> 
> thres <- 10
> x <- rlgamma3(n=10,shape=2,scale=11,thres=thres)
> dlgamma3(x,2,11,thres)
 [1] 1.669856e-04 8.744479e-05 5.673565e-05 1.624369e-04 8.018078e-05
 [6] 1.684078e-04 1.414320e-04 1.660942e-04 4.723198e-05 6.577623e-05
> dgamma3(log(x),2,1/11,thres)/x
 [1] 1.669856e-04 8.744479e-05 5.673565e-05 1.624369e-04 8.018078e-05
 [6] 1.684078e-04 1.414320e-04 1.660942e-04 4.723198e-05 6.577623e-05
> dgamma(log(x)-thres,2,11)/x
 [1] 1.669856e-04 8.744479e-05 5.673565e-05 1.624369e-04 8.018078e-05
 [6] 1.684078e-04 1.414320e-04 1.660942e-04 4.723198e-05 6.577623e-05
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>