Estimation of stress-strength reliability for the multivariate SGPII distribution

In this article, we compute and estimate the stress-strength reliability R = P(A'X + B'Y + C > 0) when X and Y are distributed independently as multivariate skewed generalized Pearson type II (SGPII) distribution, A and B are known constant vectors and C is a known scalar. For this purpose, we obtain the characteristic function of the multivariate SGPII distribution and use it for calculating R. Also, we present the maximum likelihood estimator of R and evaluate the performance of this estimator for varying sample sizes by using a simulation study. Finally, we provide a real data analysis.