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The alpha-mixture of survival functions
- Part of
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- Journal:
- Journal of Applied Probability / Volume 56 / Issue 4 / December 2019
- Published online by Cambridge University Press:
- 11 December 2019, pp. 1151-1167
- Print publication:
- December 2019
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- Article
- Export citation
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This paper presents a flexible family which we call the
$\alpha$
-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 
$\alpha$
-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 
$\alpha$
. 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.
