Bayesian estimation in weighted x gamma distribution
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Date
2017-12
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G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand)
Abstract
In the present study, a new lifetime distribution, named weighted xgamma distribution has been proposed and its distributional properties are investigated. The maximum likelihood estimates of the parameter θ have been obtained by means of Newton-Raphson method. The expressions for various distributional properties of weighted xgamma distribution including its moment generating function (mgf), cumulant generating function (cgf), characteristic function, moments etc. have been derived. The Bayes estimators of its parameter (θ), reliability function R(t) and hazard rate function h(t) are obtained using Tierney and Kadane method of approximation under two priors namely uniform and gamma. The results obtained have been illustrated by means of several randomly generated data sets from the proposed model, each sample replicated 10,000 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 to uniform prior for finding Bayes estimates of the parameter θ, reliability function R(t) and hazard rate function h(t) of the proposed weighted xgamma distribution.
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