Modified slash Birnbaum-Saunders distribution

Abstract

In this paper, we introduce an extension for the Birnbaum-Saunders (BS) distribution based on the modified slash (MS) distribution proposedby [12]. This new family of BS type distributions is obtained by replacing the usual normal distribution with the quotient of two independent random variables, one being a normal distribution in the numerator and the power of a exponential of parameter equal to two at the denominator. The resulting distribution is an extension of the BS distribution that has greater kurtosis values than the usual BS distributionand the slash Birnbaum-Saunders (SBS) distribution (see [7]). Moments and some properties are derived for the new distribution. Also, we draw inferences by the method of moments and maximum likelihood. A real data application is presented where the model fitting is implemented by using maximum likelihood estimation producing better results than the classic BS model and slash BS model.