Wrapped Birnbaum-Saunders distribution: definition and estimation

Abstract

In this work a new circular distribution called wrapped Birnbaum-Saunders was proposed. It was obtained by wrapping the classical Birnbaum Saunders distribution in a reparameterized form. For this distribution we have found expressions for their
probability density function, distribution function and trigonometric moments. We show some properties of this new distribution and obtained the maximum likelihood estimators of its two parameters, in addition, we conducted a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimators of the parameters. We also made an application to a real dataset from the Rudolf Jander’s experiments concerning the direction chosen by ants in response to a stimulus and compare its estimates via Kuiper’s statistic with those obtained from the Von Mises and Asymmetric Von Mises models. This distribution is very promising as model for asymmetric directional data.