New discrete trigonometric distributions: estimation with application to count data

Title

New discrete trigonometric distributions: estimation with application to count data

Creator

Chesneau C.; Gillariose J.; Joseph J.; Tyagi A.

Description

In this research, we contribute to the development of original discrete distributions for count data analysis. We elaborate four new and different discrete trigonometric distributions with two parameters based on a discretization of the so-called sin-Weibull, cos-Weibull, tan-Weibull, and type II tan-Weibull distributions. We investigate the advantages of the proposed distributions and their trigonometric nature for capturing count data. In particular, some fundamental distributional properties of the discrete sin-Weibull distribution are derived. Subsequently, we turn it into a statistical model. Parameter estimation by the maximum likelihood and proportion of zeros and ones methods are then discussed. A simulation study is carried out to evaluate some frequentist properties of the developed methodology. As the study focuses mainly on the practical aspect, the applicability of the proposed models is evaluated using real-count datasets from various fields. 2024 Informa UK Limited, trading as Taylor & Francis Group.

Source

International Journal of Modelling and Simulation

Date

2024-01-01

Publisher

Taylor and Francis Ltd.

Subject

Data fitting; discrete distributions; maximum likelihood estimation; reliability; trigonometric families of distributions; Weibull distribution

Coverage

Chesneau C., Department of Mathematics, LMNO, University of Caen, Caen, France; Gillariose J., Department of Statistics and Data Science, CHRIST (Deemed to be University), Karnataka, Bangalore, India; Joseph J., SCAPS, Marian College Kuttikkanam, Peermade, Idukki District, Kerala, India; Tyagi A., Department of Statistics, Chaudhary Charan Singh University, Meerut, India

Rights

Restricted Access

Relation

ISSN: 2286203; CODEN: IMSIE

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1080/02286203.2024.2315328

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85185696462&doi=10.1080%2f02286203.2024.2315328&partnerID=40&md5=d917613b0cf67a5b9b7eae8cc35172cf