Comparison of estimators and predictors based on modified weibull records: Bayesian and non-Bayesian approaches

Abstract

Based on record statistics from three-parameter modified Weibull distribution, we consider the problem of estimating the unknown parameters using Bayesian and non-Bayesian approaches. Under a continuous-discrete joint prior distribution, Bayesian estimators and confidence intervals for the shape and scale parameters involved in the underlying model are obtained. In addition, maximum likelihood prediction and Bayesian prediction (either point or interval) of future record statistics based on an informative set of records are developed. Data analyses involving records extracted from a machine used to measure burr and times to breakdown of an insulating fluid between electrodes have been performed. Finally, Monte Carlo simulations are performed to compare the methods developed here.

Keywords:

• Bayesian estimation
• Bayesian prediction
• Maximum likelihood estimation
• Maximum Likelihood prediction
• Modified Weibull distribution
• Record statistics

Acknowledgements

We would like to appreciate the constructive comments by an associate editor and two anonymous referees which improved the quality and the presentation of our results.