Abstract
This paper is intended to consider a weighted proportional hazards model and the arising mixture model from it which is called weighted frailty model and study some properties in the context of reliability theory. It is shown that the frailty random variable and the population level variable are negatively likelihood ratio dependent. Closure properties of the model with respect to some stochastic orders and some aging classes of life distributions are investigated. Finally, preservation of some stochastic orders under the structure of the model is studied. Various illustrative examples are also given.
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