Progress on a conjecture regarding the triangular distribution

Hien D. Nguyen and Geoffrey J. McLachlan

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 22, 11261-11271

Abstract: Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval can be performed via an order statistic based method. It had been conjectured that such a method can be conducted using only a constant number of likelihood function evaluations, on average, as the sample size becomes large. We prove two theorems that validate this conjecture. Graphical and numerical results are presented to supplement our proofs.

Date: 2017
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DOI: 10.1080/03610926.2016.1263742

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