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st: RE: Likelihood function of uniform distribution


From   "Rodrigo Alfaro A." <ralfaro@bcentral.cl>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Likelihood function of uniform distribution
Date   Tue, 1 Apr 2008 14:22:33 -0400

Is your uniform like: f(x) = 1/b if 0<x<1 and 0 otherwise? 
then your MLE can be obtained by sum x, then display r(max). 
Right? 
Rodrigo.



-----Mensaje original-----
De: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] En nombre de Bob Hammond
Enviado el: Martes, 01 de Abril de 2008 01:58 p.m.
Para: statalist@hsphsun2.harvard.edu
Asunto: st: Likelihood function of uniform distribution

This message is from a friend who is having trouble sending a message to
the list. Sorry if his message comes through later as a duplicate.

Hi,

In order to run a Maximum Likelihood Estimation, I need to define the
likelihood function for a uniform distribution. But I am not sure how to
define a uniform probability distribution function in Stata. For
example, I don't know how to define the following function or the
associated likelihood function in Stata:

f(x)=1 if 0<x<1
=0 otherwise.

I have tried the following commands to define the log-likelihood
function of a uniform distribution; however, I think it is NOT an
appropriate way to do it since theta is not penalized when it falls
outside the interval [0,1]:

    program myunif
    args lnf theta
    quietly replace `lnf' =ln(`theta') if $ML_y1==1
    quietly replace `lnf' =ln(1-`theta') if $ML_y1==0
    end


Also, how do you define the following triangular probability
distribution function?

f(x)= 4x if 0<x<0.5
=4-4x if 0.5<x<1
=0 otherwise.


I appreciate any help or comment in advance.

Thanks,

Mostafa

-----------------------------------------------------------------

Mostafa Beshkar
PhD Candidate
Dept of Economics, Vanderbilt University
Phone: 1(615)522-1775
Fax: 1(615)343-8495
www.people.vanderbilt.edu/~mostafa.beshkar
SSRN page:
http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=418146
--
------------------------------------------------------------------------
Bob Hammond
Department of Economics
Vanderbilt University
http://people.vanderbilt.edu/~robert.g.hammond/
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