Abstract
In the past, the proportional and additive hazard rate models have been investigated in the works. Nanda and Das (2011) introduced and studied the dynamic proportional (reversed) hazard rate model. In this paper we study the dynamic additive hazard rate model, and investigate its aging properties for different aging classes. The closure of the model under some stochastic orders has also been investigated. Some examples are also given to illustrate different aging properties and stochastic comparisons of the model.
Highlights
It is common practice in statistical analysis that covariates are often introduced to account for factors that increase the heterogeneity of a population
At first we introduce some concepts of aging notions that will be useful in the section
Example 6 below indicates that the condition of c(t) is sufficient but not a necessary one for the monotone property of Y
Summary
It is common practice in statistical analysis that covariates are often introduced to account for factors that increase the heterogeneity of a population. When the effect of a factor under study has a multiplicative (or additive) effect on the baseline hazard function, we have a proportional (or an additive) hazard model. The latter category of model is preferred in any situation. The most known Cox [1] model is that the changing conditions are assumed to act multiplicatively on the baseline hazard rate. This model has been widely used in many experiments where the time to systems’ failure depends on a group of covariates, which may be regarded as different treatments, operating conditions, heterogeneous environments, and so forth. Throughout the paper, assume that all random variables under consideration have 0 as the common left end point of their supports, and the terms increasing and decreasing stand for monotone nondecreasing and monotone nonincreasing, respectively
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