Sufficient conditions for unimodality of the positive binomial likelihood function

Dennis DeRiggi

Statistics & Probability Letters, 1994, vol. 19, issue 1, 1-4

Abstract: The likelihood function for the positive binomial with unknown parameters, N and p, is not in general unimodal. However, it is unimodal in a large class of cases (for example, when the mean of the observations is an integer). This paper develops sufficient conditions for unimodality and presents a counter-example to unimodality when these conditions do not hold. This example is given in the form of a set of observations for which the likelihood function has two critical points: a local maximum and a saddle point.

Keywords: Positive; binomial; unimodality; maximum; likelihood; estimator (search for similar items in EconPapers)
Date: 1994
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