[R] ML fit of gamma distribution to grouped data

[Prof Brian Ripley]

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)
>
> Any help is highly appreciated
>
> Thomas P.
>
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-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595