Abstract

JOARDER, ANWAR H.; OMAR, M. HAFIDZ  and  GUPTA, ARJUN K.. The Distribution of a Linear Combination ofTwo Correlated Chi-Square Variables. Rev.Colomb.Estad. [online]. 2013, vol.36, n.2, pp.209-219. ISSN 0120-1751.

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 : Bivariate Chi-square Distribution; CorrelatedChi-square Variables; Linear Combination; Characteristic Function; Cumulative Distribution; Moments.

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