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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.)
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