Circular Generalized Logistic Distributions and Its Applications

Abstract

This paper introduces three circular distributions based on inverse stereographic projection by considering three types of logistic distribution available in the literature, namely Type-I generalized logistic distribution, three parameter Type-I generalized logistic distribution and Type-II generalized logistic distribution. The proposed new models are more flexible than stereographic logistic model (DattatreyaRao et al. 2016) to the optimal modeling of circular data, can take skewness and heavy tails into account and offer a great applicability in many fields. Since one of the proposed models called circular Type-II generalized logistic distribution shows more applicability than the other proposed models. Hence, in this paper we discuss the method maximum likelihood estimation and a simulation study for circular type–II generalized logistic distribution. Finally, four circular data-sets are considered for illustrative purposes and proving that the proposed models perform well than several other circular distributions.