On distributions of ratios
推导了用分子和分母的联合特征函数表示随机变量比率的密度和分布函数的反演公式，这些公式便于数值计算并给出简单渐近展开，用数值例子验证了准确性。
Inversion formulae are derived that express the density and distribution function of a ratio of random variables in terms of the joint characteristic function of the numerator and denominator. The resulting expressions are amenable to numerical evaluation and lead to simple asymptotic expansions. The expansions reduce to known results when the denominator is almost surely positive. Their accuracy is demonstrated with numerical examples.