Maximum Likelihood Estimation of Parameters for Poisson-exponential Distribution Under Progressive Type I Interval Censoring

Abstract

This paper considers the problem of estimating the parameters of Poisson-Exponential (PE) distribution under progressive type-I interval censoring scheme. PE is a two-parameter lifetime distribution having an increasing hazard function. It has been applied in complementary risks problems in latent risks, that is in scenarios where maximum lifetime values are observed but information concerning factors accounting for component failure is unavailable. Under progressive type-I interval censoring, observations are known within two consecutively pre-arranged times and items would be withdrawn at pre-scheduled time points. This scheme is most suitable in those cases where continuous examination is impossible. Maximum likelihood estimates of Poisson-Exponential parameters are obtained via Expectation-Maximization (EM) algorithm. The EM algorithm is preferred as it has been confirmed to be a more superior tool when dealing with incomplete data sets having missing values, or models having truncated distributions. Asymptotic properties of the estimates are studied through simulation and compared based on bias and the mean squared error under different censoring schemes and parameter values. It is concluded that for an increasing sample size, the estimated values of the parameters tend to the true value. Among the four censoring schemes considered, the third scheme provides the most precise and accurate results followed by fourth scheme, first scheme and finally the second scheme.