Inference and Optimal Censoring Schemes for Progressively Censored Birnbaum-Saunders Distribution

The aim of this article is two fold. First we discuss the maximum likelihood estimators of the unknown parameters of a two-parameter Birnbaum-Saunders distribution when the data are progressively Type-II censored. The maximum likelihood estimators are obtained using the EM algorithm by exploiting the property that the BirnbaumSaunders distribution can be expressed as an equal mixture of an inverse Gaussian distribution and its reciprocal. From the proposed EM algorithm, the observed information matrix can be obtained quite easily, which can be used to construct the asymptotic confidence intervals. We perform the analysis of two real and one simulated data sets for illustrative purposes, and the performances are quite satisfactory. We further propose the use of different criteria to compare two different sampling schemes, and then find the optimal sampling scheme for a given criterion. It is observed that finding the optimal censoring scheme is a discrete optimization problem, and it is quite a computer intensive process. We examine one sub-optimal censoring scheme by restricting the choice of censoring schemes to one-step censoring schemes as suggested by Balakrishnan (2007), which can be obtained quite easily. We compare the performances of the sub-optimal censoring schemes with the optimal ones, and observe that the loss of information is quite insignificant. Kew Words and Phrases; Maximum likelihood estimation; EM algorithm; Progressive Censoring Scheme; Fisher information matrix; Inverse Gaussian distribution. SQC & OR Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata, Pin 700108, India Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Pin 208016, India. Corresponding author, e-mail: [email protected]