The Weibull Birnbaum-Saunders Distribution: Properties and Applications

Abstract: This paper introduces a new four-parameter lifetime model called the Weibull Birnbaum-Saunders distribution. This new distribution represents a more flexible model for the lifetime data. Its failure rate function can be increasing, decreasing, upside-down bathtub shaped, bathtub-shaped or modified bathtub shaped depending on its parameters. Some structural properties of the proposed model are investigated including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. The maximum likelihood estimation method is used to estimate the model parameters and the observed information matrix is determined. The flexibility of the new model is shown by means of two real data sets.