usual stochastic orderings of extreme order statistics with archimedean copula and new extended weibull random variables

In this paper, the usual stochastic order is investigated for the minimum and maximum of dependent observations from a new extended weibull distribution. the observations are coupled using archimedean copulas. some results are established for the case where certain shape parameters vary while the others are held fixed, using vector majorization techniques. since the survival function of this distribution has certain monotonicity and log‑concavity properties with respect to two of its parameters, and its distribution function is increasing and log‑concave in one of them, sufficient conditions are provided-based on existing results in the literature-for the usual stochastic ordering between sample minima or sample maxima, in terms of the heterogeneity of those two parameter vectors. finally, several examples are presented to demonstrate the applicability of the main results.