A New Class of Bivariate Survival and Reliability Models

SYNOPTIC ABSTRACT

Much research has been conducted over the last thirty years in developing and characterizing multivariate survival distributions. Typically, the multivariate distribution is derived assuming that the marginal distributions are of some specified lifetime family. In this paper, we examine a bivariate exponential model, with specified exponential marginals, and extend this model to include censored data. Closed-form joint maximum likelihood estimators (MLE) are derived and their properties studied. We also introduce a bivariate Weibull distribution derived from the exponential model. The joint MLE's are shown to give significant improvement over the marginal MLE's. In both cases, the two random variables are assumed to be linearly related in a natural way. Bivariate parameter estimation is fully developed and applied to real and simulated data.

Key Words and Phrases:

• Dirac delta
• survival
• bivariate exponential
• Weibull
• maximum likelihood