Bivariate Conway–Maxwell Poisson distributions with Given Marginals and Correlation

Seng Huat Ong; Ramesh C. Gupta; Tiefeng Ma; Shin Zhu Sim

doi:10.1007/s42519-020-00141-4

Bivariate Conway–Maxwell Poisson distributions with Given Marginals and Correlation

Seng Huat Ong, Ramesh C. Gupta, Tiefeng Ma, Shin Zhu Sim

Research output: Contribution to journal › Article › Research › peer-review

9 Citations (Scopus)

Abstract

The Conway–Maxwell Poisson (CMP) distribution is a popular model for analyzing data that exhibit under or over dispersion. In this article, we construct bivariate CMP distributions with given marginal CMP distributions and range of correlation coefficient over (− 1, 1) based on the Sarmanov family of bivariate distributions. One of the constructions is based on a general method for weighted distributions. The dependence property is examined. Parameter estimation, tests of independence and adequacy of model and a Monte Carlo power study are discussed. A real data set is used to exemplify its usefulness with comparison to other bivariate models.

Original language	English
Article number	10
Number of pages	19
Journal	Journal of Statistical Theory and Practice
Volume	15
Issue number	1
DOIs	https://doi.org/10.1007/s42519-020-00141-4
Publication status	Published - Mar 2021
Externally published	Yes

Keywords

Conway–Maxwell Poisson
Likelihood ratio test
Negative and positive correlation
Positive likelihood ratio dependence
Score test
Test of independence
Weighted distribution

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10.1007/s42519-020-00141-4

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title = "Bivariate Conway–Maxwell Poisson distributions with Given Marginals and Correlation",

abstract = "The Conway–Maxwell Poisson (CMP) distribution is a popular model for analyzing data that exhibit under or over dispersion. In this article, we construct bivariate CMP distributions with given marginal CMP distributions and range of correlation coefficient over (− 1, 1) based on the Sarmanov family of bivariate distributions. One of the constructions is based on a general method for weighted distributions. The dependence property is examined. Parameter estimation, tests of independence and adequacy of model and a Monte Carlo power study are discussed. A real data set is used to exemplify its usefulness with comparison to other bivariate models.",

keywords = "Conway–Maxwell Poisson, Likelihood ratio test, Negative and positive correlation, Positive likelihood ratio dependence, Score test, Test of independence, Weighted distribution",

author = "Ong, \{Seng Huat\} and Gupta, \{Ramesh C.\} and Tiefeng Ma and Sim, \{Shin Zhu\}",

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doi = "10.1007/s42519-020-00141-4",

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AU - Ong, Seng Huat

AU - Gupta, Ramesh C.

AU - Ma, Tiefeng

AU - Sim, Shin Zhu

PY - 2021/3

Y1 - 2021/3

N2 - The Conway–Maxwell Poisson (CMP) distribution is a popular model for analyzing data that exhibit under or over dispersion. In this article, we construct bivariate CMP distributions with given marginal CMP distributions and range of correlation coefficient over (− 1, 1) based on the Sarmanov family of bivariate distributions. One of the constructions is based on a general method for weighted distributions. The dependence property is examined. Parameter estimation, tests of independence and adequacy of model and a Monte Carlo power study are discussed. A real data set is used to exemplify its usefulness with comparison to other bivariate models.

AB - The Conway–Maxwell Poisson (CMP) distribution is a popular model for analyzing data that exhibit under or over dispersion. In this article, we construct bivariate CMP distributions with given marginal CMP distributions and range of correlation coefficient over (− 1, 1) based on the Sarmanov family of bivariate distributions. One of the constructions is based on a general method for weighted distributions. The dependence property is examined. Parameter estimation, tests of independence and adequacy of model and a Monte Carlo power study are discussed. A real data set is used to exemplify its usefulness with comparison to other bivariate models.

KW - Conway–Maxwell Poisson

KW - Likelihood ratio test

KW - Negative and positive correlation

KW - Positive likelihood ratio dependence

KW - Score test

KW - Test of independence

KW - Weighted distribution

UR - https://www.scopus.com/pages/publications/85095958149

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DO - 10.1007/s42519-020-00141-4

M3 - Article

AN - SCOPUS:85095958149

SN - 1559-8608

VL - 15

JO - Journal of Statistical Theory and Practice

JF - Journal of Statistical Theory and Practice

IS - 1

M1 - 10

ER -

Bivariate Conway–Maxwell Poisson distributions with Given Marginals and Correlation

Abstract

Keywords

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