Mixture of Birnbaum-Saunders Distributions: Identifiability, Estimation and Testing Homogeneity with Randomly Censored Data

Abstract

Random censoring is frequently utilized to analyze lifetime data in life-testing and reliability experiments. However, no published work discussed parameter estimation and testing homogeneity under random censoring for the mixture of Birnbaum-Saunders (BS) distributions, which is a useful model for describing reliability data. In this paper, first the proof of the identifiability of a finite mixture of BS distributions with g components is developed using Laplace transform of BS distributions. Then based on random censoring, parameter estimation and testing homogeneity are discussed. An EM algorithm is proposed to obtain the maximum likelihood (ML) estimates of the mixture model parameters and an EM test is implemented to test for homogeneity in the mixture of BS distributions. A Monte Carlo simulation study is conducted to evaluate the performance of the ML estimates through the bias and mean squared error. Additionally, the performance of the EM test is investigated through its size and power which are calculated by Monte Carlo simulation. Finally, an example of aircraft Windshield data is used to illustrate the estimation and testing procedures.

KEYWORDS AND PHRASES:

• Birnbaum-Saunders distribution
• censoring
• EM algorithm
• EM test
• mixture models