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From |
"Verkuilen, Jay" <JVerkuilen@gc.cuny.edu> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: Likelihood function of uniform distribution |

Date |
Tue, 1 Apr 2008 15:13:25 -0400 |

What is your friend trying to do? The problem as posed doesn't make sense to me. It strikes me that the Stata cart is being put before the theoretical horse here. -If you assert that a distribution is U(0,1), there's no free parameter to do MLE on. Is the idea trying to test whether a given RV is U(0,1)? In this case, there are numerous tests, many already in Stata, that will happily do this. Is the idea trying to estimate whether a variable is in a larger class that also includes U(0,1) as a special case? If so, check out betafit, which will estimate beta distributions. -Likelihood estimation of univariate uniform distribution with unknown upper and lower bound doesn't need anything more than sort because the MLE is just the sample min and sample max (if I recall correctly). The distribution theory for quantiles gives you nice confidence intervals. Given that this is an irregular problem, i.e., on the boundary of the parameter space, ordinary optimization theory doesn't apply and asymptotic normality won't give you sensible answers anyway. Or maybe (probably) it's something else entirely and I can't figure out what. Jay -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Bob Hammond Sent: Tuesday, April 01, 2008 1:58 PM To: statalist@hsphsun2.harvard.edu Subject: 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/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**st: RE: RE: Likelihood function of uniform distribution***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

**References**:**st: Likelihood function of uniform distribution***From:*Bob Hammond <robert.g.hammond@vanderbilt.edu>

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