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

Abstract

Let $\{X_1,\dots ,X_{N_1}\}$ and $\{Y_1,\dots ,Y_{N_2}\}$ be two sequences of interdependent heterogeneous samples, where for $i=1,\dots ,N_1,$ $X_i\sim \text{Kw-G}(x,\hat{I}{\pm }_i,{\hat{I}}_i^3;G)$ and for $i=1,\dots ,N_2,$ $Y_i\sim \text{Kw-G}(x,{\hat{I}}_i^2,\hat{I}{´}_i;H),$ where $G$ and $H$ are baseline distributions in the Kumaraswamy generalized model and $N_1$ and $N_2$ are two positive integer-valued random variables, independently of $X_i^{\prime }$s and $Y_i^{\prime }$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 ($X_{N_1:N_1}$ and $Y_{N_2:N_2}$) and the random minima ($X_{1:N_1}$ and $X_{1:N_2}$), when the sample sizes are different and random (positive).