On Determining Distributions of Products and Quotients of Random Variables Based on Quantile Functions

This paper focuses on the problem of determining the distribution functions of the product and the quotient of two independent random variables. We develop a quantile-based approach for approximating these distribution functions and analyze the corresponding approximation error. We also propose nonparametric estimators for the distribution functions of both the product and the quotient of random variables. We establish strong consistency and perform a numerical study to assess their performance in terms of bias and mean squared error.