Comment: Distribution of Quadratic Forms in Normal Random Variables—Evaluation by Numerical Integration

Rice's method [SIAM J. Sci. Stat. Comput., 1 (1980), pp. 438-448] of calculating the cumulative distribution of a random variable by numerically integrating the inversion integral for the characteristic function, described in the paper named in the title, is modified by a different choice of the saddlepoint through which the path of integration passes, a modification that renders the method efficient for values of the variable not only in the tails of the distribution, as in Rice's paper, but even in the neighborhood of its mean. It is shown how the method can also be applied to calculating the cumulative distribution of a positive-integer-valued random variable from its probability generating function.