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

Abstract

Let $\{X_{1},\ldots,X_{N_1}\}$ and $\{Y_{1},\ldots,Y_{N_2}\}$ be two sequences of interdependent heterogeneous samples, where for $i=1,\ldots,N_{1},$ $X_{i}\sim \text{Kw-G}(x, \alpha_{i}, \gamma_{i};G)$ and for $i=1,\ldots,N_{2},$ $Y_{i}\sim \text{Kw-G}(x, \beta_{i}, \delta_{i};H),$ 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 $X_{i}'$s and $Y_{i}'$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).