[R] ML fit of pareto and lognormal distributions to grouped data

[daryl yiu]

Dear list members,

I have a set of claims data, which are in ranges and the shape of the
distribution is relatively different. I have looked through R help
threads and found out that an ideal way is suggested for the gamma
distribution ML fitting for grouped data.

I just wonder if there is any method that works for lognormal or
pareto distribution?

An example would be:
Ranges<-c(0,50,100,150,200,250,300,400,500,750,1000)
Claims<-c(452,62,95,88,118,118,261,367,972,982,3024)

>From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>
>Date: Tue 28 Nov 2006 - 13:26:11 GMT
>
>
>library(stats4)
>
>ll <- function(shape, rate)
>{
>
>     z <- pgamma(breaks, shape=shape, rate=rate)
>     -sum(counts * log(diff(z)))
>
>
>}
>mle(ll, start=list(shape=1, rate=1/mean(breaks)))
>
>looks a plausible fit.
>
>On Tue, 28 Nov 2006, Thomas Petzoldt wrote:
>
>> Hello,
>>
>> we have a set of biological cell-size data, which are only available as
>> frequencies of discrete size classes, because of the high effort of
>> manual microscopic measurements.
>>
>> The lengths are approximately gamma distributed, however the shape of
>> the distribution is relatively variable between different samples (maybe
>> it's a mixture in reality).
>>
>> Is there any ML fitting (or moment-based) procedure for the gamma
>> distribution and grouped data already available in R?
>>
>> Here is a small example:
>>
>> breaks <- c(0, 20, 30, 40, 50, 60, 70, 80, 90, 100, 150)
>> mids <- c(10, 25, 35, 45, 55, 65, 75, 85, 95, 125)
>> counts <- c(87, 5, 2, 2, 1, 1, 0, 0, 1, 1)
>>

Thank you very much and any assistant is really appreciated!


-- 
Daryl Yiu