Parameter and Reliability Inferences of Inverted Exponentiated Half-Logistic Distribution under the Progressive First-Failure Censoring

Abstract

Using progressive first-failure censored samples, we mainly study the inferences of the unknown parameters and the reliability and failure functions of the Inverted Exponentiated Half-Logistic distribution. The progressive first-failure censoring is an extension and improvement of progressive censoring, which is of great significance in the field of lifetime research. Besides maximum likelihood estimation, we use Bayesian estimation under unbalanced and balanced losses: General Entropy loss function, Squared Error loss function and Linex loss function. Approximate explicit expression of Bayesian estimation is given using Lindley approximation method for point estimation and Metropolis-Hastings method for point and interval estimation. Bayesian credible intervals and asymptotic confidence intervals are derived in the form of average length and coverage probability. To show the research effects, a simulation study and practical data analysis are carried out. Finally, we discuss the optimal censoring mode under four different criteria.

Keywords

• Bayesian estimation
• maximum likelihood estimation
• Metropolis-Hastings method
• lindley approximation method
• confidence interval
• credible interval