Maximum Likelihood Estimation for a Progressively Type II Censored Generalized Inverted Exponential Distribution via EM Algorithm

Abstract

The Generalized Inverted Exponential (GIE) distribution is a mixed lifetime model used in a number of fields such as queuing theory, testing of products or components and modelling the speed of winds. The study aims to focus on the determination of maximum likelihood estimates of GIE distribution when the test units are progressively (type II) censored. The scheme permits the withdrawal of units from the life test at stages during failure. This may be due to cost and time constraints. Both Expectation- Maximization (EM) and Newton-Raphson (NR) methods have been used to obtain the maximum likelihood estimates of the GIE parameters. Also, the variance-covariance matrix of the obtained estimators has been derived. The performance of the obtained MLEs via EM method is compared with those obtained using NR method in terms of bias and root mean squared errors and confidence interval widths for different progressive type II censoring schemes at fixed parameter values of λ and θ Simulation results reveal that estimates obtained via EM approach are more robust compared to those obtained via NR algorithm. It's also noted that the bias, root mean squared errors and confidence interval widths decrease with an increase in the sample size for a fixed number of failures. A similar trend in results is observed with increase in number of failures for a fixed sample size. The results of the obtained estimators are finally illustrated on two real data sets.