March 2023 Multivariate Birnbaum–Saunders distribution based on a skewed distribution and associated EM-estimation
Filidor Vilca, Camila Borelli Zeller, Narayanaswamy Balakrishnan
Author Affiliations +
Braz. J. Probab. Stat. 37(1): 26-54 (March 2023). DOI: 10.1214/22-BJPS559


We develop here a multivariate generalization of Birnbaum–Saunders (BS) distribution based on the multivariate skew-normal distribution. Some distributional characteristics and properties are presented, as well as a simple and efficient EM algorithm for the iterative computation of the maximum likelihood (ML) estimates of model parameters, through the hierarchical representation of the proposed model. The standard errors of the maximum likelihood estimates are calculated from the observed Fisher information matrix. Moreover, by using the tools, we present a log-linear regression model, where the the ML estimates are once again obtained using an EM algorithm. Finally, simulation studies and two applications to real data sets are presented for illustrating the model and the inferential results developed here.

Funding Statement

We acknowledge the partial financial support received from FAPESP (2020/16713-0 and 2022/06421-7).


We express our sincere thanks to the Editor and the anonymous reviewers for their useful comments and suggestions on an earlier version of this manuscript which led to this much improved version.


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Filidor Vilca. Camila Borelli Zeller. Narayanaswamy Balakrishnan. "Multivariate Birnbaum–Saunders distribution based on a skewed distribution and associated EM-estimation." Braz. J. Probab. Stat. 37 (1) 26 - 54, March 2023.


Received: 1 December 2021; Accepted: 1 December 2022; Published: March 2023
First available in Project Euclid: 27 April 2023

MathSciNet: MR4580883
zbMATH: 07692848
Digital Object Identifier: 10.1214/22-BJPS559

Keywords: Birnbaum–Saunders distribution , EM algorithm , marginal and Conditional distributions , skew-normal distribution

Rights: Copyright © 2023 Brazilian Statistical Association


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Vol.37 • No. 1 • March 2023
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