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

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  • Sumith Gunasekera

Abstract

The problem of hypothesis testing and interval estimation based on the generalized variable method of the reliability parameter or the probability $$ R=\Pr (X>Y)$$ R = Pr ( X > Y ) of an item of strength $$X$$ X subject to a stress $$Y$$ Y when $$X$$ X and $$Y$$ 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. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • Sumith Gunasekera, 2015. "Generalized inferences of $$R$$ R = $$\Pr (X>Y)$$ Pr ( X > Y ) for Pareto distribution," Statistical Papers, Springer, vol. 56(2), pages 333-351, May.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:2:p:333-351
    DOI: 10.1007/s00362-014-0584-8
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    References listed on IDEAS

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    1. H. Malik, 1970. "Estimation of the parameters of the Pareto distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 15(1), pages 126-132, December.
    2. L. Jiang & A. Wong, 2008. "A note on inference for P(X > Y) for right truncated exponentially distributed data," Statistical Papers, Springer, vol. 49(4), pages 637-651, October.
    3. Chansoo Kim & Younshik Chung, 2006. "Bayesian estimation of P (Y>X) from Burr-type X model containing spurious observations," Statistical Papers, Springer, vol. 47(4), pages 643-651, October.
    4. K. Krishnamoorthy & Shubhabrata Mukherjee & Huizhen Guo, 2007. "Inference on Reliability in Two-parameter Exponential Stress–strength Model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(3), pages 261-273, May.
    5. Krishnamoorthy, K. & Lu, Fei & Mathew, Thomas, 2007. "A parametric bootstrap approach for ANOVA with unequal variances: Fixed and random models," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5731-5742, August.
    6. Bebu, Ionut & Mathew, Thomas, 2009. "Confidence intervals for limited moments and truncated moments in normal and lognormal models," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 375-380, February.
    7. Weerahandi, Samaradasa, 1987. "Testing Regression Equality with Unequal Variances," Econometrica, Econometric Society, vol. 55(5), pages 1211-1215, September.
    8. Hannig, Jan & Iyer, Hari & Patterson, Paul, 2006. "Fiducial Generalized Confidence Intervals," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 254-269, March.
    9. Eloísa Díaz-Francés & José Montoya, 2013. "The simplicity of likelihood based inferences for P(X > Y) and for the ratio of means in the exponential model," Statistical Papers, Springer, vol. 54(2), pages 499-522, May.
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    Cited by:

    1. Fatih Kızılaslan & Mustafa Nadar, 2018. "Estimation of reliability in a multicomponent stress–strength model based on a bivariate Kumaraswamy distribution," Statistical Papers, Springer, vol. 59(1), pages 307-340, March.

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