Estimation of reliability in a bivariate normal distribution with equal coefficients of variation

Abstract

In this article, we consider the problem of estimating R = P(X < Y), when X and Y have a bivariate normal distribution with common coefficients of variation. Parameters are estimated using the method of maximum likelihood, and an asymptotic confidence interval for R is derived. An example is provided to illustrate the procedure. Extensive simulation studies are carried out to examine the empirical coverage probability (ECP) and estimated mean length (EML) of the confidence interval for R.

Keywords:

• Confidence interval
• coverage probability
• estimated mean length
• Taylor series