Circular Distributions Based on Nonnegative Trigonometric Sums

Abstract

A new family of distributions for circular random variables is proposed. It is based on nonnegative trigonometric sums and can be used to model data sets which present skewness and/or multimodality. In this family of distributions, the trigonometric moments are easily expressed in terms of the parameters of the distribution. The proposed family is applied to two data sets, one related with the directions taken by ants and the other with the directions taken by turtles, to compare their goodness of fit versus common distributions used in the literature.