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

In the last decade, Diáz-Garciá and Leiva-Sánchez (2005 Diáz-Garciá, J. A., and V. Leiva-Sánchez. 2005. A new family of life distributions based on the elliptically contoured distributions. Journal of Statistical Planning and Inference 128 (2):445–57. doi: https://doi.org/10.1016/j.jspi.2003.11.007.[Crossref], [Web of Science ®] , [Google Scholar], 2007 Diáz-Garciá, J. A., and V. Leiva-Sánchez. 2007. Erratum to “A new family of life distributions based on the elliptically contoured distributions”: [J. Statist. Plann. Inference, 128 (2), (2005) 445-457]. Journal of Statistical Planning and Inference 137 (4):1512–3. doi: https://doi.org/10.1016/j.jspi.2006.06.040.[Crossref], [Web of Science ®] , [Google Scholar]) 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.