Maximum likelihood estimation of the parameters of student’s t Birnbaum-Saunders distribution: a comparative study

Abstract

In the last decade, Diáz-Garciá and Leiva-Sánchez (2005, 2007) proposed a generalized Birnbaum-Saunders distribution based on elliptically contoured distributions. A special case of this generalization is Student’s t Birnbaum-Saunders distribution. This flexible lifetime distribution generalizes both the Cauchy Birnbaum-Saunders distribution and the two-parameter Birnbaum-Saunders distribution. In this comparison paper, we discuss maximum likelihood estimation methods for the parameters of this distribution. We numerically illustrate and examine the performances of all discussed methods using extensive Monte Carlo simulations and illustrative examples. Furthermore, we analyze real-life data to assess the practical usage of the considered generalized family of distributions, and to illustrate the discussed estimation methods.

Keywords:

• Generalized Birnbaum-Saunders distribution
• Maximum likelihood estimation
• EM algorithm
• Scoring algorithm

Mathematics Subject Classification (2000):

• 62-07
• 62E99
• 62F10

Notes

1 The superscript ${}^T$ denotes the matrix transpose operator.

2 In practice, the execution time of any process depends on the available computing resources; therefore, it is important to mention that the execution times mentioned above and those that will be reported later are observed on a Desktop PC with Intel Core i7-4770 Processor and 8 GB RAM.

3 For the sake of conciseness, we did not report the simulation outcomes for this case.