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Generalized inferences of \(R\) = \(\Pr (X>Y)\) for Pareto distribution

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Abstract

The problem of hypothesis testing and interval estimation based on the generalized variable method of the reliability parameter or the probability \( R=\Pr (X>Y)\) of an item of strength \(X\) subject to a stress \(Y\) when \(X\) and \(Y\) are independent two-parameter Pareto distributed random variables is given. We discuss the use of p value as a basis for hypothesis testing. There are no exact or approximate testing procedures and confidence intervals for reliability parameter for two-parameter Pareto stress–strength model available in the literature. A simulation study is given to illustrate the proposed generalized variable method. The generalized size, generalized adjusted and unadjusted powers of the test, generalized coverage probabilities are also discussed by comparing with their classical counterparts.

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Acknowledgments

We are greatly indebted to the Editor-in-Chief and anonymous referees whose constructive and thoughtful comments on the earlier draft led to improvements in the paper’s content.

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  1. Department of Mathematics, The University of Tennessee at Chattanooga, Chattanooga, TN, 37403, USA

    Sumith Gunasekera

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  1. Sumith Gunasekera
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Correspondence to Sumith Gunasekera.

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Gunasekera, S. Generalized inferences of \(R\) = \(\Pr (X>Y)\) for Pareto distribution. Stat Papers 56, 333–351 (2015). https://doi.org/10.1007/s00362-014-0584-8

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  • DOI: https://doi.org/10.1007/s00362-014-0584-8

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