A theorem due to L. J. Gleser stating that a gamma distribution with shape parameter no greater than one is a mixed exponential distribution is extended to generalized gamma distributions introduced by E. W. Stacy as a special family of lifetime distributions containing both gamma distributions, exponential power and Weibull distributions. It is shown that the mixing distribution is a scale mix...

The two-sided and one-sided empirical Bayes test (EBT) rules for the parameter of a generalized exponential distribution with contaminated data (errors in variables) are constructed by deconvolution kernel method, respectively. Under type supersmooth error distributions errors level can be controlled situations, asymptotically optimal uniformly over class prior uniform rates convergence corresp...

Motivated by Finner et al. (2008), the asymptotic behavior of the probability density function (pdf) and the cumulative distribution function (cdf) of the generalized exponential and Maxwell distributions are studied. Specially, we consider the asymptotic behavior of the ratio of the pdfs (cdfs) of the generalized exponential and Student’s t-distributions (likewise for the Maxwell and Student’s...