Reliability functions of bivariate distributions with second kind of beta conditionals

Abstract

The purpose of this article is to study the bivariate distributions with second kind of beta conditionals, presented by Castillo and Sarabia, from a reliability point of view. The reliability functions, viz the survival function, the failure rate and mean residual life function, are derived and their monotonicity is discussed for the univariate model as well as the conditional model. Finally, Clayton’s association measure is obtained in terms of the hazard gradient and its value, in the case of our model, is derived.

Keywords:

• Failure rate
• Mean residual life function
• Hazard components
• Association measure
• Monotonicity

Acknowledgement

The author is thankful to the referee for some useful comments which enhanced the presentation.