Stress-strength reliability of generalized skewelliptical distributions and its Bayes estimation

Abstract

In this paper, we caculate the probability R ¼ PðA0Y1 þ B0Y2 þ C > 0Þ where A 2 Rp1 and B 2 Rp2 are known vectors, C is a known scalar and Y1 2 Rp1 and Y2 2 Rp2 are two independent random vectors that have generalized skew-elliptical distributions. In particular, we derive R for scale mixtures of multivariate skew normal distributions and multivariate skew normal-Cauchy distribution, then, by using some matrix variate distributions, the Bayes estimation of R for the multivariate skew normal distribution is obtained. Finally, a simulation study and a real data analysis are presented.