From: François Aucoin <frank.aucoin_at_gmail.com>

Date: Tue, 03 Jun 2008 21:54:02 -0300

R-help_at_r-project.org mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Wed 04 Jun 2008 - 00:57:20 GMT

Date: Tue, 03 Jun 2008 21:54:02 -0300

Hey,

The following is a function I wrote which generates random variables from a Kappa (2-parameter) distribution.

rkappa <- function(n,beta,alpha){

if(alpha <= 0)

stop("alpha must be greater than zero!")
if(beta <= 0)

stop("beta must be greater than zero!")
Vec <- beta*exp((1/alpha)*(log(-(alpha/(-1 +
exp(alpha*log(runif(n,0,1))))))+ alpha*log(runif(n,0,1))))
return(Vec)

*}
*

Now I would like to estimate the parameters of such a distribution using the
Maximum likelihood method.

I know that I have to minimize the following negative log likelihood
function:

Neg.Log.Like <- function(beta,alpha,x){

-(sum( log((alpha/beta)*(alpha + (x/beta)^alpha)^( -(alpha + 1)/alpha))))

*}
*

I have tried several R's functions for optimization but the results I yield
are not correct.

Is there anybody who can help me?

Thanks!

Francois Aucoin

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