1
$\begingroup$

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

$\endgroup$
0

1 Answer 1

2
$\begingroup$

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
$\endgroup$
1
  • $\begingroup$ I don't understand how to thank you. Please accept my heartfelt thanks for your great help and guidance. Regards - Katherine $\endgroup$ Apr 8, 2013 at 16:14

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.