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

Abstract

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.

Keywords

• combinación lineal
• distribución acumulada
• distribución chi cuadrado bivariada
• función característica
• momentos
• variables chi cuadrado correlacionadas