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st: RE: RE: Likelihood function of uniform distribution


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: Likelihood function of uniform distribution
Date   Wed, 2 Apr 2008 16:59:25 +0100

In addition, note that -quantile- gives a direct graphical assessment of
uniformity that does not depend on choices of bin width or kernel width
and type. 

Nick 
n.j.cox@durham.ac.uk 

Verkuilen, Jay

-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. 

Bob Hammond's friend 

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. 

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

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