Ordering properties of the smallest order statistic from Weibull G random variables

Abstract

In this paper we compare the minimums of two heterogeneous samples each following Weibull-G distribution under three scenarios. In the first scenario, the units of the samples are assumed to be independently distributed and the comparisons are carried out through vector majorization. The minimums of the samples are compared in the second scenario when the independent units of the samples also experience random shocks. The last scenario describes the comparison when the units have a dependent structure sharing Archimedean copula.

A stochastic comparison study for the smallest and largest ordered statistic from Weibull-G and Gompertz Makeham distribution

“…The stochastic comparison of such distributions are also necessary. Recently Chowdhury et al [1] have studied stochastic comparison of the smallest ordered statistic when the parameters are vector majorized. In this paper we shall use the same notations as used in Chowdhury et al [1] for convenience.…”

“…Recently Chowdhury et al [1] have studied stochastic comparison of the smallest ordered statistic when the parameters are vector majorized. In this paper we shall use the same notations as used in Chowdhury et al [1] for convenience. The Weibull-G distribution is an advanced distribution that can obtain the odds that an individual will die prior to time X, with cdf F , where these odds follow another life distribution T as observed by Cooray [6].…”