Generalized Cardioid Distributions for Circular Data Analysis

Fernanda V. Paula, Abraão D. C. Nascimento, Getúlio J. A. Amaral and Gauss M. Cordeiro
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Fernanda V. Paula: Mathematics Degree Course, Federal University of the Tocantins, Araguaína 77824-838, TO, Brazil
Abraão D. C. Nascimento: Department of Statistics, Federal University of Pernambuco, Recife 50740-540, PE, Brazil
Getúlio J. A. Amaral: Department of Statistics, Federal University of Pernambuco, Recife 50740-540, PE, Brazil
Gauss M. Cordeiro: Department of Statistics, Federal University of Pernambuco, Recife 50740-540, PE, Brazil

Stats, 2021, vol. 4, issue 3, 1-16

Abstract: The Cardioid (C) distribution is one of the most important models for modeling circular data. Although some of its structural properties have been derived, this distribution is not appropriate for asymmetry and multimodal phenomena in the circle, and then extensions are required. There are various general methods that can be used to produce circular distributions. This paper proposes four extensions of the C distribution based on the beta, Kumaraswamy, gamma, and Marshall–Olkin generators. We obtain a unique linear representation of their densities and some mathematical properties. Inference procedures for the parameters are also investigated. We perform two applications on real data, where the new models are compared to the C distribution and one of its extensions.

Keywords: circular data; extended Cardioid; trigonometric moments; weight function (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2021
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