On decomposition of a difference of independent and identically distributed random variables

Recieved: 04/22/2024

Accepted: 05/16/2024

Published: 01/31/2025

Keywords: decomposition of probability laws, characteristic function, convolution, symmetrization

To cite this article

Ushakov V.G., Ushakov N.G. On decomposition of a difference of independent and identically distributed random variables. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2025. N 1, p.68-73 https://doi.org/10.55959/MSU/0137–0782–15–2025–49–1–68–73.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Ushakov V.G. (Lomonosov Moscow State University (MSU))
(Federal Research Center "Science and Management", Russian Academy of Sciences, Moscow, Russia)
Ushakov N.G. (Norwegian University of Science and Technology, Trondheim)

Abstract

We study conditions under which components of the distribution of the difference of two independent and identically distributed random variables are determined uniquely up to a shift and reflection. This uniqueness is essential to some characterization problems. An algorithm is presented for estimation of the components when data are given in a symmetrized form.