A robust extension of the bivariate Birnbaum–Saunders distribution and associated inference

• Published in: Journal of multivariate analysis Vol. 124; pp. 418 - 435
• Main Authors: Vilca, Filidor, Balakrishnan, N., Zeller, Camila Borelli
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01-02-2014; Taylor & Francis LLC
• Subjects: Algorithms; Bivariate Birnbaum–Saunders distribution; EM-algorithm; Kurtosis; Mathematical models; Maximum likelihood method; Probability distribution; Robust estimation; Scale mixtures of normal distributions; Statistical inference; Studies; Bivariate Birnbaum–Saunders distribution; 62-XX; Scale mixtures of normal distributions; 62F10; 62Fxx; Kurtosis; Robust estimation; 62F12; 62F35; Maximum likelihood method; EM-algorithm
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1016/j.jmva.2013.11.005

We propose here a robust extension of the bivariate Birnbaum–Saunders (BS) distribution derived recently by Kundu et al. (2010). This extension is based on scale mixtures of normal (SMN) distributions that are used for modeling symmetric data. This type of bivariate Birnbaum–Saunders distribution based on SMN models is an absolutely continuous distribution whose marginals are of univariate Birnbaum–Saunders type. We then develop the EM-algorithm for the maximum likelihood (ML) estimation of the model parameters, and illustrate the obtained results with a real data and display the robustness feature of the estimation procedure developed here.