Re: Question about multimodal parameter estimation

nelson wrote:

i have some data and looking at them i suppose are generated by a gamma
distribution plus a normal distribution, in fact the look like this figure:

*
**
**
***
***
**** ****
******* ********
******************************

(i hope you can read it :) )

How can i estimate the parameter of the distribution of my data? I read
about MLE, but i can't find example that uses multimodal ditributions...

What you want is to estimate a mixture density, in this case a density
p (x) = a_1 p_1 (x) + a_2 p_2 (x) where p_1 and p_2 and gamma and
normal
density functions, respectively, and a_1 and a_2 are positive factors
(the so-called mixing weights) such that a_1 + a_2 = 1.

You can do direct MLE on p, the free parameters being a_1 and a_2
in addition to the parameters for the gamma and normal densities.
There is also the so-called expectation-maximization algorithm,
which is very simply to implement if you already have MLE implemented
for each mixture component.

Check and see if the R project (http://www.r-project.org)
already has something for this problem. Try asking on the r-help
mailing list.

FWIW
Robert Dodier

.

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