Maximum likelihood methods for fitting the Burr Type XII distribution to multiply (progressively) censored life test data

This paper develops mathematical and computational methodology for fitting, by the method of maximum likelihood (ML), the Burr Type XII distribution to multiply (or progressively) censored life test data. Mathematical and expressions are given for approximating the asymptotic variances and covariances of the ML estimates (MLEs) of the parameters of the Burr Type XII distribution. A rigorous mathematical analysis is undertaken to investigate the existence and uniqueness of the MLEs for arbitrary sample data. The methodology of this paper is applied to progressively censored sample data arising in a life test experiment.