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From |
Bob Hammond <robert.g.hammond@vanderbilt.edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Likelihood function of uniform distribution |

Date |
Tue, 01 Apr 2008 12:57:50 -0500 |

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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**Follow-Ups**:**Re: st: Likelihood function of uniform distribution***From:*"Stas Kolenikov" <skolenik@gmail.com>

**st: RE: Likelihood function of uniform distribution***From:*"Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>

**st: RE: Likelihood function of uniform distribution***From:*"Rodrigo Alfaro A." <ralfaro@bcentral.cl>

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