Beta Distribution Bootstrap Confidence Intervals Exponential Distribution Gamma Distribution Normal Distribution Stress-Strength Uniform Distribution
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Pliska Studia Mathematica Bulgarica, Vol. 16, No 1, (2004), 159p-170p
In the area of stress-strength models there has been a large amount of work as regards estimation of the probability R = Pr(X<Y) when X and Y are independent random variables belonging to the same univariate family of distributions. In this paper we propose an estimate of this quantity based on a simple property of the uniform distribution. We illustrate the use of the estimate with bootstrap confidence intervals for four commonly known distributions (normal, exponential, gamma and beta).