Generalized multivariate Birnbaum-Saunders distributions and related inferential issues

Authors:
Debasis Kundu;N. Balakrishnan;Ahad Jamalizadeh
Affiliations:
Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Pin 208016, India;Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1;Department of Statistics, Faculty of Mathematics & Computer, Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran
Venue:
Journal of Multivariate Analysis
Year:
2013

Citing 7
Cited 1

Modified moment estimation for the two-parameter Birnbaum--Saunders distribution

Computational Statistics & Data Analysis
Lifetime analysis based on the generalized Birnbaum-Saunders distribution

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On the hazard function of Birnbaum-Saunders distribution and associated inference

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Estimation of the Birnbaum-Saunders regression model with current status data

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Bivariate Birnbaum-Saunders distribution and associated inference

Journal of Multivariate Analysis
Estimation of extreme percentiles in Birnbaum-Saunders distributions

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Shape and change point analyses of the Birnbaum-Saunders-t hazard rate and associated estimation

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

Journal of Multivariate Analysis

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Abstract

Birnbaum and Saunders introduced in 1969 a two-parameter lifetime distribution which has been used quite successfully to model a wide variety of univariate positively skewed data. Diaz-Garcia and Leiva-Sanchez [8] proposed a generalized Birnbaum-Saunders distribution by using an elliptically symmetric distribution in place of the normal distribution. Recently, Kundu et al. [13] introduced a bivariate Birnbaum-Saunders distribution, based on a transformation of a bivariate normal distribution, and discussed its properties and associated inferential issues. In this paper, we construct a generalized multivariate Birnbaum-Saunders distribution, by using the multivariate elliptically symmetric distribution as a base kernel for the transformation instead of the multivariate normal distribution. Different properties of this distribution are obtained in the general case. Special emphasis is placed on statistical inference for two particular cases: (i) multivariate normal kernel and (ii) multivariate-t kernels. We use the maximized log-likelihood values for selecting the best kernel function. Finally, a data analysis is presented for illustrative purposes.