A New Bivariate Distribution with One Marginal Defined on the Unit Interval

Daya K. Nagar; Saralees Nadarajah; Idika E. Okorie

doi:10.1007/s40745-017-0111-6

A New Bivariate Distribution with One Marginal Defined on the Unit Interval

Daya K. Nagar, Saralees Nadarajah, Idika E. Okorie

Mathematics

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

7 Scopus citations

Abstract

The most flexible bivariate distribution to date is proposed with one variable restricted to [0, 1] and the other taking any non-negative value. Various mathematical properties and maximum likelihood estimation are addressed. The mathematical properties derived include shape of the distribution, covariance, correlation coefficient, joint moment generating function, Rényi entropy and Shannon entropy. For interval estimation, explicit expressions are derived for the information matrix. Illustrations using two real data sets show that the proposed distribution performs better than all other known distributions of its kind.

Original language	British English
Pages (from-to)	405-420
Number of pages	16
Journal	Annals of Data Science
Volume	4
Issue number	3
DOIs	https://doi.org/10.1007/s40745-017-0111-6
State	Published - 1 Sep 2017

Keywords

Beta distribution
Extended beta function
Gamma distribution

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10.1007/s40745-017-0111-6

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title = "A New Bivariate Distribution with One Marginal Defined on the Unit Interval",

abstract = "The most flexible bivariate distribution to date is proposed with one variable restricted to [0, 1] and the other taking any non-negative value. Various mathematical properties and maximum likelihood estimation are addressed. The mathematical properties derived include shape of the distribution, covariance, correlation coefficient, joint moment generating function, R{\'e}nyi entropy and Shannon entropy. For interval estimation, explicit expressions are derived for the information matrix. Illustrations using two real data sets show that the proposed distribution performs better than all other known distributions of its kind.",

keywords = "Beta distribution, Extended beta function, Gamma distribution",

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AU - Nadarajah, Saralees

AU - Okorie, Idika E.

N1 - Funding Information: The research work of DKN was supported by the Sistema Universitario de Investigación, Universidad de Antioquia under the project no. IN10231CE. The authors would like to thank the Editor and the three referees for careful reading and comments which greatly improved the paper. Publisher Copyright: © 2017, Springer-Verlag Berlin Heidelberg.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - The most flexible bivariate distribution to date is proposed with one variable restricted to [0, 1] and the other taking any non-negative value. Various mathematical properties and maximum likelihood estimation are addressed. The mathematical properties derived include shape of the distribution, covariance, correlation coefficient, joint moment generating function, Rényi entropy and Shannon entropy. For interval estimation, explicit expressions are derived for the information matrix. Illustrations using two real data sets show that the proposed distribution performs better than all other known distributions of its kind.

AB - The most flexible bivariate distribution to date is proposed with one variable restricted to [0, 1] and the other taking any non-negative value. Various mathematical properties and maximum likelihood estimation are addressed. The mathematical properties derived include shape of the distribution, covariance, correlation coefficient, joint moment generating function, Rényi entropy and Shannon entropy. For interval estimation, explicit expressions are derived for the information matrix. Illustrations using two real data sets show that the proposed distribution performs better than all other known distributions of its kind.

KW - Beta distribution

KW - Extended beta function

KW - Gamma distribution

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JO - Annals of Data Science

JF - Annals of Data Science

IS - 3

ER -

A New Bivariate Distribution with One Marginal Defined on the Unit Interval

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Keywords

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