Bayesian inference for modified Weibull distribution under simple step‐stress model based on type‐I censoring
Qasim Ramzan, Muhammad Amin, Muhammad Faisal
Abstract
Abstract In this paper, we consider a simple step‐stress accelerated life test (SSALT) model under the tampered random variable (TRV) model for the modified Weibull distribution (MWD) with type‐I censoring. We consider the classical and Bayesian estimation methods for the estimation of unknown parameters of the MWD model. In the classical scenario, we derive the maximum likelihood estimates (MLEs) and approximate confidence intervals (ACIs) for model parameters. Also, a parametric bootstrap resampling technique is used to derive the bootstrap confidence intervals. Under the Bayesian paradigm, the point estimates of the unknown parameters for different symmetric, asymmetric, and balanced loss functions and highest posterior density (HPD) credible intervals (CIs) are derived via Gibbs within metropolis‐hasting sampling procedure. A simulation study is conducted to compare the performance of Bayesian estimates with MLEs. Moreover, we also compare the precision of considered CIs. Finally, a real application is considered for illustration purpose.