Estimation of P[Y < X] for some spesific Distribution

Hasanpour, Zeinab (2017) Estimation of P[Y < X] for some spesific 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, Reliability is concerned with censored data. We have discussed and examined in this dissertation the estimation of R = P[Y < X] when X and Y random variable fromare the specifc distributions such as independent Weibull distributions with different scale parameters but having the same shape parameter. The maximum likelihood estimator and the approximate maximum likelihood estimator of R have obtained. For maximum likelihood estimator of R the asymptotic distributions are used. Based on asymptotic distributions the confidence intervals of R such the Bootstrap are obtained confidence interval. We obtained Bayes estimator of R under non-proper prior function and also the corresponding credible interval for R. With Monte Carlo simulation methods we compared the proposed method. In the end part, by numerical analysis method, the data analysis performed.

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