Variance residual life function in discrete random ageing

Springer Science and Business Media LLC - 2012
M. Khorashadizadeh1, A. H. Rezaei Roknabadi1, G. R. Mohtashami Borzadaran1
1Department of Statistics Ordered and Spatial Data Center of Excellence School of Mathematical Sciences Ferdowsi, University of Mashhad, Mashhad, Iran

Tóm tắt

The random variable X t = X − t¦X ≥ t, which is called the residual life random variable, has gathered the attention of most researchers in reliability. The mean and the variance of this variable in continuous distribution have been studied by several authors. But, in discrete case, only in recent years, some studies have been done for the mean of this variable. In this paper, we define and study the properties of variance of T k = T − k¦T ≥ k where T is a discrete random variable. Besides similar results for discrete and continuous lifetime distributions, relationships with its mean, monotonicity and the associated ageing classes of distributions are obtained for discrete cases. Furthermore, some characterization results about the class of increasing (decreasing) variance residual life distributions based on mean residual life and residual coefficient of variation, are presented and the lower and upper bound for them are achieved.

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