Table of Contents
Journal of Computational Engineering
Volume 2015 (2015), Article ID 801652, 12 pages
Research Article

An Estimate of the Probability Density Function of the Sum of a Random Number of Independent Random Variables

Dipartimento di Ingegneria, Università degli Studi di Napoli “Parthenope”, Centro Direzionale, Isola C4, 80143 Napoli, Italy

Received 30 October 2014; Revised 1 March 2015; Accepted 3 March 2015

Academic Editor: Liudong Xing

Copyright © 2015 Angelo Gifuni et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new estimate of the probability density function (PDF) of the sum of a random number of independent and identically distributed (IID) random variables is shown. The sum PDF is represented as a sum of normal PDFs weighted according to the PDF. The analytical model is verified by numerical simulations. The comparison is made by the Chi-Square Goodness-of-Fit test.