A Multivariate Lifetime Model of Marshal-Olkin Type
Manuel Franco1, Debasis Kundu2, Juana-Maria Vivo3
1Statistics and Operations Research, University of Murcia, Murcia, Spain; 2Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India; 3Quantitative Methods for Economy, University of Murcia, Murcia, Spain

In many practical problems, multivariate lifetime data frequently arise, and in these situations it is important to consider different multivariate distributions that could be used to model such multivariate lifetime data.

A bivariate distribution model of Marshall-Olkin type was recently introduced by Sarhan and Balakrishnan (2007), which has been extended to the multivariate case by Franco and Vivo (2010). The construction of this model is based on a procedure of latent random variables, formed from generalized exponential (GE) random variables with an exponential latent factor, that GE distribution was introduced by Gupta and Kundu (1999) as an alternative to the well known gamma or Weibull distribution in analyzing many lifetime data (also see Gupta and Kundu, 2007).

Recently, Kundu and Gupta (2010) introduced the modified bivariate Sarhan and Balakrishnan (MBSB) distribution using similar approach as the Sarhan and Balakrishnan model with an GE latent factor.

In this work, we study a multivariate lifetime model as an extension of the MBSB distribution given by Kundu and Gupta (2010). We discuss some distributional properties and related aspects of this MMSB distribution, such as the ageing and dependence on its components, and its series and parallel systems formed from them.

Keywords: Multivariate lifetime distributions; Generalized exponential distribution; Multivariate failure rate; Series and parallel systems

Biography: Juana-Maria Vivo is a Professor of the University of Murcia. Her research interests are among others distribution theory, reliability analysis, generalized mixtures, distributions with bounded support, ageing and dependence, multivariate lifetime models.