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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? * * 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/

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

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

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