Progress on a conjecture regarding the triangular distribution

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.

Acknowledgments

We thank the two anonymous reviewers for their useful comments, which have significantly improved the exposition of the article.