Weibull distribution model

SUMMARY

In estimating the parameters of a probability distribution in survival analysis, Bayesian mechanism examines the nature uncertainty and provide a judicious framework for studying such problems. In this study, we have considered Bayesian estimators of the parameter of the Weibull distribution under the linear exponential (LINEX) loss function and generalized entropy loss function (GELF) using the Gamma conjugate prior for the shape parameter and the Jeffreys’ non-informative prior for the scale parameter. The posterior distribution for the estimation of Weibull parameters,  and  is in a form which cannot be reduced to a closed form, making it tedious to evaluate the posterior distribution in order to obtain the Bayesian estimators. The Bayesian estimators were obtained using Lindley's approximation techniques under the two loss functions.

The simulation study presented in Chapter 4 shows that the MSE’s decreasing as the sample size increases in all cases. From Table 1-3, we observe that the MSE’s of the MLE is higher than the MSE’s of the Bayesian estimators under LINEX and GELF. We can then say that the non-classical Bayesian estimates are better than the classical Maximum Likelihood estimates (MLE). It is also observed that the Bayesian estimator under the LINEX loss function has the smallest value of MSE in all cases, which makes it the best estimator for both the shape and scale parameters of the Weibull distribution.