An EM-Algorithm for Estimating the Lifetime Distribution with Long Terms Survival Data

Abstract

We are interested here in the estimation of the lifetime distribution by using the right censored observations taking into account the probability p that a censored item might contract the interest event after the right censoring. This type of censorship is known in the literature as long-term survival item. We assume that the lifetime follows a log-normal distribution with parameters μ and σ . An EM-algorithm is developed so as to estimate the 2 parameters μ, σ and p. Simulations indicate good accurate and robustness results. The EM- algorithm is then applied to the Cameroonian custom services data set in order to estimate the distribution of the return delays of the Global Position System (GPS). The EM-algorithm leads to accurate results of the parameters involved with smaller mean squared error.