Ordering results for random maxima and minima from two dependent Kumaraswamy-generalized distributed samples

Let X1, …, XN1 and Y1, …, YN2 be two sequences of interdependent heterogeneous samples, where for i=1, …, N1, Xi∼Kw−G (x, αi, γi;G) and for i=1, …, N2, Yi∼Kw−G (x, βi, δi;H), where G and H are baseline distributions in the Kumaraswamy-generalized model and N1 and N2 are two positive integer-valued random variables, independently of Xi′s and Yi′s, respectively. In this article, we establish several stochastic orders, such as usual stochastic, hazard rate, reversed hazard rate, dispersive and likelihood ratio orders between the random maxima (XN1: N1 and YN2: N2) and the random minima (X1: N1 and X1: N2), when the sample sizes are different and random (positive).