Statistical Analysis of the Log-Normal Distribution under Type-II Progressive Hybrid Censoring Schemes

Abstract

In this article, we obtain the maximum likelihood estimators (MLEs) and approximate maximum likelihood estimators (AMLEs) of the parameters, from a two-parameter log-normal distribution based on the adaptive Type-II progressive hybrid censoring scheme, which was introduced by Ng et al. (2009) for life testing or reliability experiment. In order to compare the results, we calculate corresponding estimators of the Type-II progressive hybrid censoring scheme. In particular, we provide computational formulas of the expected total test time and the expected number of failures for each scheme. We also compute the observed Fisher information matrix and use them to obtain the asymptotic confidence intervals. A simulation study carries out to evaluate the bias and mean square error of the MLEs and AMLEs from the two above-mentioned schemes. Finally, we present a numerical example to illustrate the methods of inference discussed here.

Keywords:

• Approximate maximum likelihood estimator
• Hybrid censoring
• Log-normal distribution
• Maximum likelihood estimator
• Type-II progressive censoring

Mathematics Subject Classification:

• 62N01
• 62N02
• 62N03
• 62N05

Acknowledgments

The authors thank the Associate Editor and the anonymous referee immensely for a careful reading of the article.