Density functions of the bivariate chi-square distribution

The purpose of this paper is to present a practical approach to solving simultaneous testing and estimation problems faced by the experimenter. New forms of the bivariate Chi-square distribution are introduced which afford straightforward computer programming. An approximation which reduces the general type of dependency to a specific form is suggested, reinforced by strong theoretical justification. Finally, the bivariate Chi-square density function is used to find the density function of a linear combination of independent Chi-square random variables