Estimation of P[Y < X] for Three Parameter Generalized Rayleigh Distribution

Maleki, Roghayyeh (2017) Estimation of P[Y < X] for Three Parameter Generalized Rayleigh Distribution. Masters thesis, University of Mohaghegh Ardabili.

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Abstract

The reliability of the study during the remaining life esistance people or systems or length of time that a system is working in a time interval is checked to the profit and loss over the remaining life due to be expressed.This attention to reliability shows. In this thesis we deal with the estimate of R=P(Y<X) in which the random variables X and Y are the stress and strength, respectively and the both random variabies are from three-paramrter generalized Rayleigh distribution with the same scale and locations parameters but different shape parameters. In addition, modified maximum likelihood estimation of R was discussed. Then obtained the asymptotic distribution of the modified maximum likelihood estimator of R and based on, the asymptotic confidence interval of R was discussed. Also Bayes estimator of R under prior function obtained as the corresponding credible interval for R. In the end part the data analysis performed by numerical analysis method

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