# Three Parameter Pearson 5 Distribution

I need some information about the following -

Is "Pearson Type III Distribution" as given in lmomco package (CRAN R) same as Three Parameter Pearson 5 Distribution?

If not, how do I estimate the parameters of Three Parameter Pearson 5 Distribution?

Regards

Katherine

From wikipedia:

The Pearson type III distribution is a [shifted] gamma distribution or chi-squared distribution.

Then the answer is: no, it is not the same as the "three-parameter Pearson 5 distribution".

The Pearson type V distribution is a shifted inverse-gamma distribution. Its density is given in the following entry

http://www.mathwave.com/help/easyfit/html/analyses/distributions/pearson5.html

The parameters of the Pearson type V distribution can be estimated as usual, using your favourite optimisation algorithm.

An example in R

rm(list=ls())
library(MCMCpack)

# Simulated data
set.seed(1000)
n <- 250
data <- rinvgamma(n, shape = 5, scale = 5) -1
hist(data)

# log-likelihood
ll <- function(par){
if(par[3]<min(data) & par[1]>0 & par[2]>0) return( -sum(log(dinvgamma(data-par[3],par[1],par[2]))) )
else return(Inf)
}

# Optimisation step
optim(c(5,5,-1.5),ll)

# MLE of (alpha,beta,mu), mu is the shift parameter

optim(c(5,5,-1.5),ll)\$par

• I don't understand how to thank you. Please accept my heartfelt thanks for your great help and guidance. Regards - Katherine Apr 8, 2013 at 16:14