A remark on the distribution of products of independent normal random variables-Reference-Cited by-同舟云学术

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A remark on the distribution of products of independent normal random variables

Published:2021-03-10 Issue:3 Volume:10 Page:30-37
ISSN:2544-9125
Container-title:Science, Technology and Innovation
language:
Short-container-title:Sci. Tech., Innov

Author:

Szczepański Jerzy¹

Affiliation:

1. Jagiellonian University Faculty of Mathematics and Computer Science

Abstract

We present a proof of the explicit formula of the probability density function of the product of normally distributed independent random variables using the multiplicative convolution formula for Meijer G functions.

Publisher

University of Applied Sciences in Tarnow, Poland

Link

https://stijournal.pl/gicid/pdf/01.3001.0014.7861

Reference11 articles.

1. Bateman H, Erdélyi A. Higher transcendental functions. Vol. 1. New York: McGraw-Hill; 1953.

2. Beals R, Szmigielski J. Meijer G-functions: a gentle introduction. Notices of the American Mathematical Society. 2013;60(7):866–872. doi: http://dx.doi.org/10.1090/notimanid1016

3. Carter BD, Springer MD. The distribution of products, quotients and powers of independent H-function variates. SIAM Journal on Applied Mathematics. 1977;33(4):542– 558. doi: https://doi.org/10.1137/0133036

4. Craig CC. On the frequency function of XY. The Annals of Mathematical Statistics. 1936;7(1):1–15

5. Craig CC. On frequency distributions of the quotient and of the product of two statistical variables. The American Mathematical Monthly. 1942;49(1):24–32. doi: https://doi.org/10.1080/00029890.1942.11991175

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