The Distribution of a Linear Combination ofTwo Correlated Chi-Square Variables

The Distribution of a Linear Combination ofTwo Correlated Chi-Square Variables

The distribution of the linear combination of two chi-square variables is known if the variables are independent. In this paper, we derive the distribution of positive linear combination of two chi-square variables when they are correlated through a bivariate chi-square distribution. Some properties...

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Main Authors: ANWAR H. JOARDER, M. HAFIDZ OMAR, ARJUN K. GUPTA
Format: Article
Language:English
Published: Universidad Nacional de Colombia 2013-12-01
Series:Revista Colombiana de Estadística
Subjects:
combinación lineal
distribución acumulada
distribución chi cuadrado bivariada
función característica
momentos
variables chi cuadrado correlacionadas
Online Access:http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512013000200002&lng=en&tlng=en
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spelling doaj-35ceae874c1842dab232514e5a250d1f2020-11-25T01:35:18ZengUniversidad Nacional de Colombia Revista Colombiana de Estadística0120-17512013-12-01362209219S0120-17512013000200002The Distribution of a Linear Combination ofTwo Correlated Chi-Square VariablesANWAR H. JOARDER0M. HAFIDZ OMAR1ARJUN K. GUPTA2King Fahd University of Petroleum and MineralsKing Fahd University of Petroleum and MineralsBowling Green State UniversityThe distribution of the linear combination of two chi-square variables is known if the variables are independent. In this paper, we derive the distribution of positive linear combination of two chi-square variables when they are correlated through a bivariate chi-square distribution. Some properties of the distribution, namely, the characteristic function, cumulative distribution function, raw moments, mean centered moments, coefficients of skewness and kurtosis are derived. Results match with the independent case when the variables are uncorrelated. The graph of the density function is presented.http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512013000200002&lng=en&tlng=encombinación linealdistribución acumuladadistribución chi cuadrado bivariadafunción característicamomentosvariables chi cuadrado correlacionadas
collection DOAJ
language English
format Article
sources DOAJ
author ANWAR H. JOARDER
M. HAFIDZ OMAR
ARJUN K. GUPTA
spellingShingle ANWAR H. JOARDER
M. HAFIDZ OMAR
ARJUN K. GUPTA
The Distribution of a Linear Combination ofTwo Correlated Chi-Square Variables
Revista Colombiana de Estadística
combinación lineal
distribución acumulada
distribución chi cuadrado bivariada
función característica
momentos
variables chi cuadrado correlacionadas
author_facet ANWAR H. JOARDER
M. HAFIDZ OMAR
ARJUN K. GUPTA
author_sort ANWAR H. JOARDER
title The Distribution of a Linear Combination ofTwo Correlated Chi-Square Variables
title_short The Distribution of a Linear Combination ofTwo Correlated Chi-Square Variables
title_full The Distribution of a Linear Combination ofTwo Correlated Chi-Square Variables
title_fullStr The Distribution of a Linear Combination ofTwo Correlated Chi-Square Variables
title_full_unstemmed The Distribution of a Linear Combination ofTwo Correlated Chi-Square Variables
title_sort distribution of a linear combination oftwo correlated chi-square variables
publisher Universidad Nacional de Colombia
series Revista Colombiana de Estadística
issn 0120-1751
publishDate 2013-12-01
description The distribution of the linear combination of two chi-square variables is known if the variables are independent. In this paper, we derive the distribution of positive linear combination of two chi-square variables when they are correlated through a bivariate chi-square distribution. Some properties of the distribution, namely, the characteristic function, cumulative distribution function, raw moments, mean centered moments, coefficients of skewness and kurtosis are derived. Results match with the independent case when the variables are uncorrelated. The graph of the density function is presented.
topic combinación lineal
distribución acumulada
distribución chi cuadrado bivariada
función característica
momentos
variables chi cuadrado correlacionadas
url http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512013000200002&lng=en&tlng=en
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