Abstract
This paper develops a Bayesian analysis of the scale parameter in the Weibull distribution with a scale parameter  θ  and shape parameter  β (known). For the prior distribution of the parameter involved, inverted Gamma distribution has been examined. Bayes estimates of the scale parameter, θ  , relative to LINEX loss function are obtained. Comparisons in terms of risk functions of those under LINEX loss and squared error loss functions with their respective alternate estimators, viz: Uniformly Minimum Variance Unbiased Estimator (U.M.V.U.E) and Bayes estimators relative to squared error loss function are made. It is found that Bayes estimators relative to squared error loss function dominate the alternative estimators in terms of risk function.
Highlights
Sometimes, in practical situations either from past experience or from some reliable sources, one may have a guessed estimate of the parameter which can be treated as a prior information. Thompson (1968a, b) introduced the idea of shrinking usual estimators towards point as well as interval guess value to get the improved estimators
This paper develops a Bayesian analysis of the scale parameter in the Weibull distribution with a scale parameter and shape parameter
It is found that Bayes estimators relative to squared error loss function dominate the alternative estimators in terms of risk function
Summary
We make comparisons of the obtained estimators in terms of risk functions of those under Linex loss and squared error loss function. Once Bayes estimators under Linex loss function and squared error loss function have been obtained, comparisons in terms of their risk functions have been made, their relative efficiencies are computed. Some conclusions based on computations and graphs regarding relative efficiencies for some effective intervals will help us to know what estimators performs better than alternative estimators in terms of effective interval relative to Linex loss function than those relative to squared error loss function. We observe that for an increase in the magnitude of “a”, ttytytyty. Some conclusions based on graphs regarding effective interval reveals that for the Weibull distribution, ˆM performs better than alternative estimators in terms of effective interval relative to squared error loss function than those relative to Linex error loss function
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