A note on an approximation and estimation of distribution function of difference of random variables
Year: 2025
Type: article
Abstract: In this paper we deal with the problem of determining the distribution function of the difference of two independent random variables. Using a quantile-based representation we obtain an approximation of distribution function of difference of two independent random variables. Next, we obtain the error of this approximation. Finally, we use the approximation to present a non-parametric estimator for the distribution function of difference of two independent random variables. Moreover, we prove the strong consistency of this estimator and we carry out a numerical simulation to evaluate the bias and mean squared error of the estimator. Also we compare our estimator with the classical empirical distribution function.
Source: Statistical Papers
Authors: Dagmara Dudek, Anna Kuczmaszewska
Institution: Lublin University of Technology
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,890
OpenAlex ID: W4416411326