Bayes estimation in weibull distribution
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Date
2016-06
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G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand)
Abstract
In the present study, Bayes estimators of the parameters α and β of 2-parameter Weibull distribution and its reliability function R(t) have been obtained using 2 priors by means of Tierney and Kadane method and the results obtained are illustrated by means of several random samples generated from the above said distribution through R software and two real data sets. It is revealed that when α is known, Bayes estimate (2.0074) of β is more precise for prior 2 compared to prior 1 at α=2.0, whereas Bayes estimate (0.5138) of R(t) is more precise for prior 2 compared to prior 1 at α=1.5 and initial time t=1.2. Further when β is known, Bayes estimates (1.5100) and (0.6446) of α and reliability function R(t=1.2) respectively are more precise for prior 2 compared to prior 1 at β=3.0. In case both parameters α and β are unknown, Bayes Risks of the estimates of α and R(t) under SELF are smaller for prior 2 compared to prior 1 for first three random samples generated from Weibull distribution with parameters (α=1.5, β=2.0); (α=1.5, β=3.0) and (α=2.0, β=2.5) respectively whereas Risk of the estimate of β is smaller for Prior 1 in case of these first three samples. Moreover, for the random sample generated from Weibull distribution with α=2.5, β=2.5, the risks of the estimates of β and R(t) are smaller for prior 1 compared to prior 2 and the risk of the estimate of α is smaller for prior 2 compared to prior 1. For two real data sets, prior 2 is superior to prior 1 for obtaining Bayes estimates (5.2788 and 4.8120) of α and Bayes estimates (191.6974 and 365.9996) of β which supports the conclusions drawn from the data generated through R software. Therefore, it is safer to use prior 2 compared to prior 1 for getting Bayes estimates of parameters α and β of 2 parameter Weibull distribution.
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