Inference for Log-Gamma Distribution Based on Progressively Type-II Censored Data

Abstract

We discuss the maximum likelihood estimates (MLEs) of the parameters of the log-gamma distribution based on progressively Type-II censored samples. We use the profile likelihood approach to tackle the problem of the estimation of the shape parameter κ. We derive approximate maximum likelihood estimators of the parameters μ and σ and use them as initial values in the determination of the MLEs through the Newton–Raphson method. Next, we discuss the EM algorithm and propose a modified EM algorithm for the determination of the MLEs. A simulation study is conducted to evaluate the bias and mean square error of these estimators and examine their behavior as the progressive censoring scheme and the shape parameter vary. We also discuss the interval estimation of the parameters μ and σ and show that the intervals based on the asymptotic normality of MLEs have very poor probability coverages for small values of m. Finally, we present two examples to illustrate all the methods of inference discussed in this paper.

Keywords:

• Approximate maximum likelihood estimators
• EM algorithm
• Extreme value distribution
• Fisher information
• Fixed-point iteration
• Maximum likelihood estimators
• Modified EM algorithm
• Monte Carlo simulations
• Newton–Raphson method
• Normal distribution
• Pivotal quantities
• Probability coverages

Mathematics Subject Classification:

• 62F10
• 65C05