FAILURE DISTRIBUTIONS WITH DECREASING MEAN RESIDUAL LIFE.
SYSTEM DEVELOPMENT CORP SANTA MONICA CALIF
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It is well known that the class of distributions with decreasing mean residual life DMR contains the class of distributions with increasing hazard rate IHR. The study of DMR distributions has received little attention in the literature. Starting with a random variable T 0, which has all its moments, and with distribution function F sub 0 x, we can construct a sequence of distribution functions with the following properties 1 F sub o x is DMR implies that F sub k x is DMR, k1,2,... . 2 F sub 0 x is DMR implies that F sub k x converges either to a singular distribution or to an exponential distribution. 3 The members of the sequence F sub k x are all identically exponentially distributed if and only if for some k or 1, F sub k t F sub k-1 t. Author
- Statistics and Probability