Inferences for Weibull parameters under progressively first-failure censored data with binomial random removals

Abstract

In this paper, the Bayesian and non-Bayesian estimation of a two-parameter Weibull lifetime model in presence of progressive first-failure censored data with binomial random removals are considered. Based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators, two-sided approximate confidence intervals for the unknown parameters are constructed. Using gamma conjugate priors, several Bayes estimates and associated credible intervals are obtained relative to the squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. A Bayesian approach is developed using Markov chain Monte Carlo techniques to generate samples from the posterior distributions and in turn computing the Bayes estimates and associated credible intervals. To analyze the performance of the proposed estimators, a Monte Carlo simulation study is conducted. Finally, a real data set is discussed for illustration purposes.

Statistical Analysis of Alpha Power Exponential Parameters Using Progressive First-Failure Censoring with Applications

“…To acquire the maximum likelihood estimates (MLEs) of α and δ, one should maximize the objective function in (7) with respect to these unknown parameters.…”

“…Ashour et al [6] studied the inferences and optimal schemes for the Nadarajah-Haghighi distribution. Ashour et al [7] studied both Bayesian and non-Bayesian estimations for the Weibull parameters using binomial random removals. Shi and Shi [8] considered an inference for the inverse power Lomax distribution.…”