Mathematical Problems in Engineering
Volume 2005 (2005), Issue 1, Pages 101-111
doi:10.1155/MPE.2005.101
Reliability for some bivariate beta distributions
Department of Statistics, University of Nebraska, Lincoln 68583, NE, USA
Received 24 June 2004
Copyright © 2005 Saralees Nadarajah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In the area of stress-strength models there has been a large
amount of work as regards estimation of the reliability R=Pr(X<Y). The algebraic form for R=Pr(X<Y) has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same
univariate family. In this paper, we consider forms of R when (X,Y) follows a bivariate distribution with dependence between
X and Y. In particular, we derive explicit expressions for R when the joint distribution is bivariate beta. The calculations
involve the use of special functions.