Differential Approach to Cardioid Distribution

Abstract

Jeffreys (1961) introduced Cardioid distribution and used it to modeling directional spectra of ocean waves.Here an attempt is made to derive pdf of cardioid model as a solution of a second order non homogeneouslinear differential equation having constant coefficients with certain initial conditions. We also arrive atnew unimodal and symmetric distribution on real line from Cardioid model induced by Mobiustransformation called Cauchy type models.

Keywords: Circular model, Mobius transformation, Cardioid and Uniform distributions, Cauchy typemodels.