TY - JOUR
T1 - The Distribution of a Linear Combination of Two Correlated Chi-Square Variables
AU - Joarder, Anwarul Haque
AU - Omar, Hafidz
AU - Gupta, Vinod Kumar
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
M3 - Article
SN - 0120-1751
JO - Revista Colombiana de Estadistica
JF - Revista Colombiana de Estadistica
ER -