Some hydrological quantities such as the rainfall intensity, which is defined as the quotient of the rainfall depth to the rainfall duration, are based on functions of random variables. At this point, the probability distribution of that quantity arises. Then one may take this distribution into account for the exact statistical inference without referring to a simulation study. There are a lot of works on the exact distributions of functions of random variables in the literature. One case is for the Pareto distributed random variables. Pareto distribution and its upper truncated version have many applications in hydrological modelling. In this paper, the exact distributions of the product, sum and quotient of two independently distributed upper truncated Pareto random variables are obtained. Although the probability density functions of the product and quotient are obtained in elementary mathematical functions, that for the sum is obtained in terms of a special function. Some characteristics of these functions such as moments and percentiles can be easily obtained. The distributions of the quotient and the sum are applied on a rainfall data set from hydraulic efficiency research of green roofs. The parameters are estimated by the method of maximum likelihood. The theoretical results of this paper may also be useful to other practitioners of the upper truncated Pareto distribution.

一些水文量（例如降雨强度）是基于随机变量的函数，降雨强度定义为降雨深度与降雨持续时间的商。此时，出现了该数量的概率分布。这样一来，就可以将这种分布考虑在内，以进行精确的统计推断，而无需参考模拟研究。文献中有很多关于随机变量函数的精确分布的著作。一种情况是帕累托分布随机变量。帕累托分布及其上截断形式在水文模拟中有许多应用。本文获得了两个独立分布的上截断的帕累托随机变量的乘积，和与商的精确分布。尽管乘积和商的概率密度函数是在基本数学函数中获得的，但总和的概率密度函数是根据特殊函数获得的。这些函数的某些特性（例如矩和百分位数）可以轻松获得。商和之和的分布应用于绿化屋顶水力效率研究的降雨数据集。通过最大似然法估计参数。本文的理论结果也可能对上截断的帕累托分布的其他实践者有用。商和之和的分布应用于绿化屋顶水力效率研究的降雨数据集。通过最大似然法估计参数。本文的理论结果也可能对上截断的帕累托分布的其他实践者有用。商和之和的分布应用于绿化屋顶水力效率研究的降雨数据集。通过最大似然法估计参数。本文的理论结果也可能对上截断的帕累托分布的其他实践者有用。