Exact distribution of the sum of two correlated chi-square variables and its application

Kuwait Journal of Science

ANWAR H. JOARDER¹  M. HAFIDZ OMAR¹ 

[1] Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

关键词: Bivariate chi-square distribution;    characteristic function;    correlated chi-square variables;    cumulative distribution function;    sum of correlated chi-square variables.;   

DOI  :  

学科分类：社会科学、人文和艺术（综合）

来源: Kuwait University * Academic Publication Council

【 摘 要 】

The exact distribution of the sum of two chi-square random variables is known if the variables are independent. We derive the exact distribution of the sum of two correlated chi-square variables when they are correlated through a bivariate chi-square distribution. The distribution is important in estimating the common variance of a bivariate normal population. Some properties of the distribution, namely, the characteristic function, cumulative distribution function, raw moments, mean centered moments, coefficient of skewness and kurtosis are derived. The graph of the density function is also presented.

【 授权许可】

Unknown