Bayesian inference of Weibull distribution for right and interval censored data

The main purpose of this work is to draw comparisons between the classical maximum likelihood and the Bayesian estimators on the parameters, the survival function and hazard rate of the Weibull distribution when the data under consideration are right and interval censored. We have considered the survival data to follow Weibull distribution due to its adaptability in fitting time-to-failure of a very widespread multiplicity to multifaceted mechanisms in the field of life-testing and survival analysis. In Bayesian estimations, prior distributions as well as loss functions need to be specified. The prior distributions can be obtained via previous study in relation to the current study or by soliciting information from experts. We have considered in this study, different types of priors, such as, Jeffreys prior, extension of Jeffreys’ prior information, gamma priors and have also proposed a generalised non-informative prior. The loss functions considered in this study are asymmetric and symmetric loss functions. Lindley’s approximation procedure is used in the Bayesian estimation approach to reduce the ratio of integrals in the posterior distributions which cannot be obtained in close forms. When we consider both the scale and shape parameters under the right and interval censored data, we observed that the estimate of the shape parameter under the maximum likelihood method cannot be obtained in close form; therefore, a numerical approach known as Newton-Raphson has been employed to estimate the shape parameter. The mean squared errors and mean absolute biases of the estimates under Bayes and its maximum likelihood counterpart are examined through simulation study under several conditions to evaluate the performance of both methods. Overall, it has been observed that, the proposed Bayesian estimation under the generalised non-informative prior performed better than the other estimators for the scale and shape parameters, the survival function and hazard rate. The Bayesian estimator via the generalised non-informative prior occurred largely with the linear exponential loss function followed by general entropy loss function.

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