Parameter Estimation for the Two-Parameter Exponentiated Weibull Distribution Based on Multiply Type-I Censored Data

Abstract

Multiple Type-I censoring represents that all the test units are terminated at different times. Hence, it is the general form of Type-I censoring, which is common in life testing experiments due to simplicity. Besides, the two-parameter exponentiated Weibull (EW) distribution could describe both the nonmonotone and monotone failure rates. Obviously, it is extremely meaningful to estimate the EW parameters with multiply Type-I censored data. The problem is studied in this paper. First, the point estimates are presented using a maximum likelihood estimate (MLE) and least-square estimate (LSE), respectively. Next, the asymptotic normality of MLE and bootstrap method based on LSE are used to construct the confidence interval (CI) for EW parameters. Furthermore, the Bayesian model is provided by fusing kinds of prior information. Two different prior distributions are discussed to obtain the Bayesian estimate (BE) and modified Bayesian estimate (MBE) together with the corresponding Bayesian credible intervals for EW parameters. Different point estimates and CIs are compared through a Monte Carlo simulation study. It is demonstrated that the MLE outperforms LSE and MBE is superior to others. Finally, a published dataset is analyzed to illustrate the application of these methods. The results agree with the simulation conclusions. Therefore, the study in this paper is useful and effective.

Keywords

• Exponentiated Weibull distribution
• Bayesian estimate
• least-square estimate
• maximum likelihood estimate
• multiple Type-I censoring