The alpha-mixture of survival functions

Abstract

This paper presents a flexible family which we call the -mixture of survival functions. This family includes the survival mixture, failure rate mixture, models that are stochastically closer to each of these conventional mixtures, and many other models. The -mixture is endowed by the stochastic order and uniquely possesses a mathematical property known in economics as the constant elasticity of substitution, which provides an interpretation for α. We study failure rate properties of this family and establish closures under monotone failure rates of the mixture's components. Examples include potential applications for comparing systems. © Applied Probability Trust 2019.