Mathematical Problems in Engineering
Volume 2005 (2005), Issue 2, Pages 151-163
doi:10.1155/MPE.2005.151
Reliability for some bivariate gamma distributions
Department of Statistics, University of Nebraska, Lincoln 68583, NE, USA
Received 23 July 2004; Revised 23 November 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 gamma. The calculations
involve the use of special functions.