The cosine geometric distribution with count data modeling

Christophe Chesneau; Hassan S Bakouch; Tassaddaq Hussain; Bilal A Para

doi:10.1080/02664763.2019.1711364

The cosine geometric distribution with count data modeling

J Appl Stat. 2020 Jan 9;48(1):124-137. doi: 10.1080/02664763.2019.1711364. eCollection 2021.

Authors

Christophe Chesneau¹, Hassan S Bakouch², Tassaddaq Hussain³, Bilal A Para⁴

Affiliations

¹ LMNO, University of Caen-Normandie, Caen, France.
² Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.
³ Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur (AJ&K), Pakistan.
⁴ Department of Statistics, Government Degree College Anantnag (J&K), Anantnag, India.

Abstract

In this paper, a new two-parameter discrete distribution is introduced. It belongs to the family of the weighted geometric distribution (GD), with the feature of using a particular trigonometric weight. This configuration adds an oscillating property to the former GD which can be helpful in analyzing the data with over-dispersion, as developed in this study. First, we present the basic statistical properties of the new distribution, including the cumulative distribution function, hazard rate function and moment generating function. Estimation of the related model parameters is investigated using the maximum likelihood method. A simulation study is performed to illustrate the convergence of the estimators. Applications to two practical datasets are given to show that the new model performs at least as well as some competitors.

Keywords: 60E05; 62E15; Weighted geometric distribution; cumulative distribution function; data with over-dispersion.