Maximum Likelihood Estimation Of Parameters For Poisson-Exponential Distribution Under Progressive Type I Interval Censoring

Abstract

The problem of estimating the parameters of Poisson-Exponential distribution under progressive type-I interval censoring is considered. Previously, researchers have considered maximum likelihood estimation under the progressive type-I interval censoring scheme for various distribution, but no research has considered Poisson-Exponential. Poisson-Exponential 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, which can be experienced in fields such as public health. 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type I interval censoring, observations are known within two consecutively pre-arranged times and items would be withdrawn at pre-scheduled time points. Progressive type-I interval censoring scheme is most suitable in those cases where the continuous examination is impossible. Based on progressive type I interval censored data, the Maximum Likelihood Estimates of Poisson-Exponential parameters are obtained via the Expectation-Maximization algorithm. The Expectation-Maximization 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. In this study, the estimates derived are compared through simulation 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 p(3) provides the most precise and accurate results followed by p(4), p(1) and lastly p(2).