Inference based on progressive Type I interval censored data from log-normal distribution

ABSTRACT

This article considers inference for the log-normal distribution based on progressive Type I interval censored data by both frequentist and Bayesian methods. First, the maximum likelihood estimates (MLEs) of the unknown model parameters are computed by expectation-maximization (EM) algorithm. The asymptotic standard errors (ASEs) of the MLEs are obtained by applying the missing information principle. Next, the Bayes’ estimates of the model parameters are obtained by Gibbs sampling method under both symmetric and asymmetric loss functions. The Gibbs sampling scheme is facilitated by adopting a similar data augmentation scheme as in EM algorithm. The performance of the MLEs and various Bayesian point estimates is judged via a simulation study. A real dataset is analyzed for the purpose of illustration.

KEYWORDS:

• Data augmentation
• EM algorithm
• Gibbs sampling
• LINEX loss function
• Missing information principle

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N05

Acknowledgments

The authors thank two referees and an associate editor for their critical comments and helpful suggestions, which led to a considerable improvement over the earlier version of the manuscript. This work is partially supported from the project “Optimization and Reliability Modeling” funded by Indian Statistical Institute.