Bayesian estimation of the survival characteristics for weighted Xgamma distribution
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Date
2020-10
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G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand)
Abstract
In present study a weighted version of xgamma distribution is introduced and studied, which is a life time distribution. We work out its length biased version and distributional properties. The Maximum Likelihood estimates of the parameter ϴ have been obtained by means of Newton Rapson method. With the help of Tierney and Kadane method of approximation, we have obtained Bayes estimators of ϴ, Survival function, failure rate function and Mean time to failure under two priors namely gamma and uniform. The result obtained have been illustrated by means of several randomly generated data sets from the proposed distribution each replicated 10000 times. The Bayes risks have been evaluated by SELF. A real life data set has also been used to estabilish its utility. It is concluded that gamma prior is superior to uniform prior for finding the Bayes estimates of the parameter ϴ, Survival function, failure rate function and Mean time to failure of the length biased version of the proposed distribution.