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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-

The distribution of the ratio of random variables is of interest in statistical analysis in biological and physical sciences, econometrics, and ranking and selection [

In the areas of deployment, connectivity, and capacity, multihop systems have a number of advantages over traditional communication networks. Relaying techniques enable network connectivity where traditional architectures are impractical due to location constraints and can be applied to cellular, wireless local area networks (WLANs) and hybrid networks. The performance analysis of multihop wireless communication systems operating in fading channels has been an important field of research in the past few years [

The main contribution of this paper is the derivation of useful closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) of ratio of product of two random variables and random variable. Among the rest, these expressions can be used as general theoretical tool in the performance analysis of wireless communication systems since the product of random variables in nominator can represent signal envelope which suffers from fading and shadowing while the random variable in denominator can represent CCI envelope. Therefore, the ratio of such random variables is signal-to-interference ratio (SIR). Rayleigh, Nakagami-

In this section, statistical analysis of ratio of products of two random variables and random variable,

Cumulative distribution function can be obtained by definition as

In the case of Rayleigh distribution, the PDFs of random variables are given by

The Weibull random variables are distributed according to

The Nakagami-

The

Applying the procedure described at the beginning of this section with the aid of [

The PDFs and CDFs of

PDF and CDF of

PDF and CDF of

PDF and CDF of

PDF and CDF of

Multihop (

Multihop transmission.

Depending on the nature of the radio propagation environment, the statistical behaviour of signal envelope can be described with different distributions. This is reason why our analysis includes so many statistical models. The Rayleigh model is frequently used to describe multipath fading with no direct line-of-sight (LOS) path [

The product of random variables,

PDF of

The PDF and CDF of ratio of product of two random variables and random variable

This work was supported by the Ministry of Science of Serbia within the Project TR-32023.