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arXiv · 1405.4529

Inference on P(Y<X) in Bivariate Rayleigh Distribution

Abbas Pak·Nayereh Bagheri Khoolenjani·Ali Akbar Jafari
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Abstract

This paper deals with the estimation of reliability $R=P(Y<X)$ when $X$ is a random strength of a component subjected to a random stress $Y$ and $(X,Y)$ follows a bivariate Rayleigh distribution. The maximum likelihood estimator of $R$ and its asymptotic distribution are obtained. An asymptotic confidence interval of $R$ is constructed using the asymptotic distribution. Also, two confidence intervals are proposed based on Bootstrap method and a computational approach. Testing of the reliability based on asymptotic distribution of $R$ is discussed. Simulation study to investigate performance of the confidence intervals and tests has been carried out. Also, a numerical example is given to illustrate the proposed approaches.

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Abbas Pak, Nayereh Bagheri Khoolenjani, Ali Akbar Jafari. 2014-05-18. Inference on P(Y<X) in Bivariate Rayleigh Distribution. https://arxiv.org/abs/1405.4529

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