Maximum likelihood estimation of triangular and polygonal distributions

Nguyen, Hien D. and McLachlan, Geoffrey J. (2016) Maximum likelihood estimation of triangular and polygonal distributions. Computational Statistics and Data Analysis, 102 23-36. doi:10.1016/j.csda.2016.04.003

Author Nguyen, Hien D.
McLachlan, Geoffrey J.
Title Maximum likelihood estimation of triangular and polygonal distributions
Journal name Computational Statistics and Data Analysis   Check publisher's open access policy
ISSN 0167-9473
Publication date 2016-10-01
Year available 2016
Sub-type Article (original research)
DOI 10.1016/j.csda.2016.04.003
Open Access Status Not Open Access
Volume 102
Start page 23
End page 36
Total pages 14
Place of publication Amsterdam, Netherlands
Publisher Elsevier
Collection year 2017
Language eng
Abstract Triangular distributions are a well-known class of distributions that are often used as elementary example of a probability model. In the past, enumeration and order statistics-based methods have been suggested for the maximum likelihood (ML) estimation of such distributions. A novel parametrization of triangular distributions is presented. The parametrization allows for the construction of an MM (minorization–maximization) algorithm for the ML estimation of triangular distributions. The algorithm is shown to both monotonically increase the likelihood evaluations, and be globally convergent. Using the parametrization is then applied to construct an MM algorithm for the ML estimation of polygonal distributions. This algorithm is shown to have the same numerical properties as that of the triangular distribution. Numerical simulations are provided to demonstrate the performances of the new algorithms against established enumeration and order statistics-based methods.
Keyword Triangular distributions
Polygonal distributions
Minorization-maximization algorithms
Mixture models
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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