STATISTICAL INFERENCE FOR A STEP-STRESS PARTIALLY ACCELERATED LIFE TEST MODEL BASED ON PROGRESSIVELY TYPE-II-CENSORED DATA FROM LOMAX DISTRIBUTION

• Published in: Journal of applied statistical science Vol. 21; no. 4; p. 307
• Main Authors: El-Sagheer, Rashad M, Ahsanullah, Mohamed
• Format: Journal Article
• Language: English
• Published: Hauppauge Nova Science Publishers, Inc 2013
• Subjects: Acceleration; Asymptotic methods; Bayesian analysis; Computer simulation; Confidence intervals; Density; Estimates; Markov analysis; Mathematical models; Monte Carlo simulation; Samples; Statistical methods; Studies
• ISSN: 1067-5817

In this article, the maximum likelihood (ML), Bayes, and parametric bootstrap methods are used for estimating the unknown parameters of Lomax distribution and the acceleration factor based on progressively type-II censored schemes under step-stress partially accelerated life test (SSPALT) model. Based on normal approximation to the asymptotic distribution of MLEs, the approximate confidence intervals (ACIs) for the parameters and the acceleration factor are derived. In addition, two bootstrap confidence intervals are also proposed. The classical Bayes estimates cannot be obtained in explicit form, so we propose to apply the Markov chain Monte Carlo (MCMC) technique to compute the Bayes estimates of the parameters and the acceleration factor. Gibbs within the Metropolis-Hasting algorithm is applied to generate MCMC samples from the posterior density function. Based on the generated samples, the Bayes estimates and highest posterior density credible intervals of the unknown parameters have been computed. Finally, analysis of a simulated data set has also been presented to illustrate the proposed estimation methods.