Abstract
We propose a procedure to obtain accurate confidence intervals for the stress-strength reliability R = P (X > Y) when (X, Y) is a bivariate normal distribution with unknown means and covariance matrix. Our method is more accurate than standard methods as it possesses a third-order distributional accuracy. Simulations studies are provided to show the performance of the proposed method relative to existing ones in terms of coverage probability and average length. An empirical example is given to illustrate its usefulness in practice.
Highlights
2 y y where σ x,σ y > 0, and ρ < 1
( ) where Φ (⋅) is the cumulative distribution is the variance of the difference of the two function of the variables; and standard θ = μx, normal distribution; σ μ y
An empirical example is provided to illustrate the usefulness of the method in practice
Summary
2 y y where σ x ,σ y > 0 , and ρ < 1. Nguimkeu et al [1] recently proposed a third-order method for inference about R for the case where the normal variables X and Y are independents; that is, ρ = 0. In financial risk-management one may want to compare the stock returns from two companies. If these companies operate in the same industry the prices of these stocks are likely to be correlated. We modify the procedure proposed by Nguimkeu et al [1] to account for possible correlation between the stress and the strength variables when they are sampled from normal populations. The Wald method is based on the statistic (q) defined by
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