Exponential approximations for two classes of aging distributions (Q797896)

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.