Statistical Modelling with Birnbaum-Saunders Distribution
Nuri Celik *
Department of Mathematics, Gebze Technical University, 41400, Kocaeli, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this article, it is assumed that the distribution of the error terms is the Birnbaum-Saunders distribution in the process of one-way ANOVA. The Birnbaum-Saunders distribution has been widely used in reliability analysis especially in fatigue-life models. In reliability analysis, nonnormal distribution is much more common than the normal distribution. We obtain the estimation of the parameters og interest by maximum likelihood method. We also propose new test statistics based on these estimators . The efficiencies of the maximum likelihood estimators and the Type I errors obtained by using the proposed estimators are compared with normal theory via Monte Carlo simulation study. At the end of the study, the real life example is given just for the illustration of the method.
Keywords: Statistical modelling, Birnbaum-Saunders distribution, ANOVA, maximum likelihood