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Bayesian Estimation of the Survival Characteristics for a Special Case of Weighted X gamma Distribution

Jai Prakash, Vinod Kumar

Abstract


In the present study, a weighted version of the xgamma distribution is introduced and its special case i.e. length biased version, isstudied as a lifetime distribution. With the help of Tierney and Kadane method of approximation, we have obtained Bayes estimators of the parameter θ, Survival function, Failure rate function and Mean time to failure under three Priors namely Gamma,Uniform and Mukherjee-Islam. The results obtained have been illustrated employing several randomly generated data sets from the proposed distribution each replicated 10000 times. The Bayes risks have been evaluated by using Squared Error Loss Function (SELF). A real-life data set has also been used to establish its utility.It is concluded that Gamma Prior is superior among the other two Priorsfor finding the Bayes estimates of the parameterθ, Survival function, Failure rate function and Mean time to failure of the length biased version of the proposed distribution.


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References


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