On Classical Inference of a Flexible Semi-Parametric Class of Distributions Under a Joint Balanced Progressive Censoring Scheme

The paper deals with the estimation procedures for the proportional hazard class of distributions under a two-sample balanced joint progressive censoring scheme. The baseline hazard function is assumed to be piecewise constant, instead of any specific form. This adds flexibility to the proposed model, and the shape of the underlying hazard function is completely data-driven. Since the complicated form of the likelihood function does not yield closed-form estimators, we propose a variant of the Expectation-Maximization algorithm, known as the Expectation Conditional Maximization (ECM) algorithm, for obtaining maximum likelihood estimates of the model parameters. This leads to explicit expressions for the iterative constrained maximization steps of the algorithm. An extension to the case when the cut points are unknown has also been considered for dealing with problems involving real data. Simulation results and illustrations using real data have also been presented.