Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 841092, 10 pages
http://dx.doi.org/10.1155/2012/841092
Research Article

Statistical Analysis of Ratio of Random Variables and Its Application in Performance Analysis of Multihop Wireless Transmissions

Edis Mekić,1 Mihajlo Stefanović,2 Petar Spalević,3 Nikola Sekulović,2 and Ana Stanković2

1Department of Computer Technologies, State University of Novi Pazar, Vuka Karadzica bb, 36300 Novi Pazar, Serbia
2Faculty of Electronic Engineering, University of Nis, Aleksandra Medvedeva 14, 18000 Nis, Serbia
3Faculty of Technical Sciences, University of Kosovska Mitrovica, Kneza Milosa 7, 38220 Kosovska Mitrovica, Serbia

Received 2 July 2011; Accepted 19 October 2011

Academic Editor: Kue-Hong Chen

Copyright © 2012 Edis Mekić 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.

Abstract

The distributions of random variables are of interest in many areas of science. In this paper, the probability density function (PDF) and cumulative distribution function (CDF) of ratio of products of two random variables and random variable are derived. Random variables are described with Rayleigh, Nakagami-m, Weibull, and 𝛼 - 𝜇 distributions. An application of obtained results in performance analysis of multihop wireless communication systems in different transmission environments described in detail. The proposed mathematical analysis is also complemented by various graphically presented numerical results.