## Exponential approximations for two classes of aging distributions.(English)Zbl 0546.60021

Let X be a random variable with $$\mu =EX$$ and $$\mu_ 2=EX^ 2$$. The authors introduce two classes of distribution functions with finite $$\mu$$ and $$\mu_ 2$$ and point out the upper bounds for $$| 1-F(x)-\exp (- x/\mu)|$$ with F from these classes in terms of $$\rho =| (\mu_ 2/2\mu)-1|.$$ These bounds are the weakest among the commonly studied classes of aging distribution functions.
Reviewer: V.M.Kruglov

### MSC:

 60E15 Inequalities; stochastic orderings 60K10 Applications of renewal theory (reliability, demand theory, etc.)

### Keywords:

aging distribution functions
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