Abstract
This paper describes the numerical evaluation of the mathematical forms of the distribution of the product , , , where x 1 and x 2 follow a bivariate normal distribution . The methods used are general for the evaluation of distribution functions found by the inversion of the characteristic function of the random variable. Special cases of the distribution are the central and noncentral γ 2 with one degree of freedom. The distribution function of the product is expressed as an integral involving sine, cosine, and exponential functions. A computer code has been written to generate the distribution function table for fixed δ 1 δ 2, and ρ. The computer code uses Romberg integration and Euler's transformation to evaluate the infinite integrals. Several tables are provided to support the accuracy of the computer code.
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