On the Exact Distribution of the Difference Between Two Chi-Square Variables

Anwar H. Joarder; M. Hafidz Omar

doi:10.1007/s40840-022-01373-2

On the Exact Distribution of the Difference Between Two Chi-Square Variables

Anwar H. Joarder
, M. Hafidz Omar^*

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

4 Scopus citations

Abstract

We have reviewed the development of the exact distribution of the difference of two independently and identically distributed chi-square variables and presented derivations based on moment generating function and also by convolution method. We have also developed general moment results of the difference of two independently and identically distributed random variables and applied these to chi-square random variables. Some properties of the distribution, namely moment generating function, mean centered moments, coefficient of skewness and kurtosis, and cumulative distribution function, have been derived. The graph of the density functions has been presented. We conclude the paper with directions for further research along the line.

Original language	English
Pages (from-to)	505-522
Number of pages	18
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	45
DOIs	https://doi.org/10.1007/s40840-022-01373-2
State	Published - Sep 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.

Keywords

Chi-square distribution
Cumulative distribution function, moments, control chart
Difference of chi-square variables

ASJC Scopus subject areas

General Mathematics

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10.1007/s40840-022-01373-2

Cite this

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title = "On the Exact Distribution of the Difference Between Two Chi-Square Variables",

abstract = "We have reviewed the development of the exact distribution of the difference of two independently and identically distributed chi-square variables and presented derivations based on moment generating function and also by convolution method. We have also developed general moment results of the difference of two independently and identically distributed random variables and applied these to chi-square random variables. Some properties of the distribution, namely moment generating function, mean centered moments, coefficient of skewness and kurtosis, and cumulative distribution function, have been derived. The graph of the density functions has been presented. We conclude the paper with directions for further research along the line.",

keywords = "Chi-square distribution, Cumulative distribution function, moments, control chart, Difference of chi-square variables",

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T1 - On the Exact Distribution of the Difference Between Two Chi-Square Variables

AU - Joarder, Anwar H.

AU - Omar, M. Hafidz

PY - 2022/9

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N2 - We have reviewed the development of the exact distribution of the difference of two independently and identically distributed chi-square variables and presented derivations based on moment generating function and also by convolution method. We have also developed general moment results of the difference of two independently and identically distributed random variables and applied these to chi-square random variables. Some properties of the distribution, namely moment generating function, mean centered moments, coefficient of skewness and kurtosis, and cumulative distribution function, have been derived. The graph of the density functions has been presented. We conclude the paper with directions for further research along the line.

AB - We have reviewed the development of the exact distribution of the difference of two independently and identically distributed chi-square variables and presented derivations based on moment generating function and also by convolution method. We have also developed general moment results of the difference of two independently and identically distributed random variables and applied these to chi-square random variables. Some properties of the distribution, namely moment generating function, mean centered moments, coefficient of skewness and kurtosis, and cumulative distribution function, have been derived. The graph of the density functions has been presented. We conclude the paper with directions for further research along the line.

KW - Chi-square distribution

KW - Cumulative distribution function, moments, control chart

KW - Difference of chi-square variables

UR - https://www.scopus.com/pages/publications/85138053927

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DO - 10.1007/s40840-022-01373-2

M3 - Article

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SN - 0126-6705

VL - 45

SP - 505

EP - 522

JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

ER -

On the Exact Distribution of the Difference Between Two Chi-Square Variables

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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