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

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Edis Mekić ◽  
Mihajlo Stefanović ◽  
Petar Spalević ◽  
Nikola Sekulović ◽  
Ana Stanković
Keyword(s):  
Performance Analysis ◽  
Communication Systems ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Wireless Communication Systems ◽  
Multihop Wireless ◽  
Ratio Of Random Variables ◽  
Probability Density Function Pdf

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, andα-μdistributions. 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.

scholarly journals The Distribution of the Ratio of the Products of Two Independentα-μVariates and Its Application in the Performance Analysis of Relaying Communication Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Ana Matović ◽  
Edis Mekić ◽  
Nikola Sekulović ◽  
Mihajlo Stefanović ◽  
Marija Matović ◽  
...  
Keyword(s):  
Distribution Function ◽  
Performance Analysis ◽  
Probability Density Function ◽  
Theoretical Analysis ◽  
Communication Systems ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Wireless Communication Systems ◽  
Multihop Wireless ◽  
Probability Density Function Pdf

We present novel general, simple, exact, and closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) of the ratio of the products of two independentα-μvariates, where all variates have identical values of alpha parameter. Obtained results are applied in analysis of multihop wireless communication systems in different fading transmission environments. The proposed theoretical analysis is also complemented by various graphically presented numerical results.

scholarly journals On Distribution Characteristics of a Fuzzy Random Variable

2018 ◽  
Vol 47 (2) ◽  
pp. 53-67 ◽  
Author(s):  
Jalal Chachi
Keyword(s):  
Probability Theory ◽  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Distribution Characteristics ◽  
Fuzzy Random Variables ◽  
Fuzzy Random

In this paper, rst a new notion of fuzzy random variables is introduced. Then, usingclassical techniques in Probability Theory, some aspects and results associated to a randomvariable (including expectation, variance, covariance, correlation coecient, etc.) will beextended to this new environment. Furthermore, within this framework, we can use thetools of general Probability Theory to dene fuzzy cumulative distribution function of afuzzy random variable.

Bias-corrected Estimation of the Density of a Conditional Expectation in Nested Simulation Problems

2021 ◽  
Vol 31 (4) ◽  
pp. 1-36
Author(s):  
Ran Yang ◽  
David Kent ◽  
Daniel W. Apley ◽  
Jeremy Staum ◽  
David Ruppert
Keyword(s):  
Conditional Expectation ◽  
Cumulative Distribution Function ◽  
Empirical Distribution ◽  
Random Variables ◽  
Cumulative Distribution ◽  
Prior Work ◽  
Density Deconvolution ◽  
Computational Budget ◽  
Naive Estimator ◽  
Probability Density Function Pdf

Many two-level nested simulation applications involve the conditional expectation of some response variable, where the expected response is the quantity of interest, and the expectation is with respect to the inner-level random variables, conditioned on the outer-level random variables. The latter typically represent random risk factors, and risk can be quantified by estimating the probability density function (pdf) or cumulative distribution function (cdf) of the conditional expectation. Much prior work has considered a naïve estimator that uses the empirical distribution of the sample averages across the inner-level replicates. This results in a biased estimator, because the distribution of the sample averages is over-dispersed relative to the distribution of the conditional expectation when the number of inner-level replicates is finite. Whereas most prior work has focused on allocating the numbers of outer- and inner-level replicates to balance the bias/variance tradeoff, we develop a bias-corrected pdf estimator. Our approach is based on the concept of density deconvolution, which is widely used to estimate densities with noisy observations but has not previously been considered for nested simulation problems. For a fixed computational budget, the bias-corrected deconvolution estimator allows more outer-level and fewer inner-level replicates to be used, which substantially improves the efficiency of the nested simulation.

scholarly journals A Technique for Computing the PDFs and CDFs of Nonnegative Infinitely Divisible Random Variables

2011 ◽  
Vol 48 (01) ◽  
pp. 217-237 ◽  
Author(s):  
Mark S. Veillette ◽  
Murad S. Taqqu
Keyword(s):  
Distribution Function ◽  
Laplace Transform ◽  
Cumulative Distribution Function ◽  
Stable Distribution ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Infinitely Divisible ◽  
The Laplace Transform ◽  
Laplace Transform Inversion ◽  
Probability Density Function Pdf

We present a method for computing the probability density function (PDF) and the cumulative distribution function (CDF) of a nonnegative infinitely divisible random variable X. Our method uses the Lévy-Khintchine representation of the Laplace transform Ee-λX = e-ϕ(λ), where ϕ is the Laplace exponent. We apply the Post-Widder method for Laplace transform inversion combined with a sequence convergence accelerator to obtain accurate results. We demonstrate this technique on several examples, including the stable distribution, mixtures thereof, and integrals with respect to nonnegative Lévy processes.

scholarly journals A Technique for Computing the PDFs and CDFs of Nonnegative Infinitely Divisible Random Variables

2011 ◽  
Vol 48 (1) ◽  
pp. 217-237 ◽  
Author(s):  
Mark S. Veillette ◽  
Murad S. Taqqu
Keyword(s):  
Distribution Function ◽  
Laplace Transform ◽  
Cumulative Distribution Function ◽  
Stable Distribution ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Infinitely Divisible ◽  
The Laplace Transform ◽  
Laplace Transform Inversion ◽  
Probability Density Function Pdf

We present a method for computing the probability density function (PDF) and the cumulative distribution function (CDF) of a nonnegative infinitely divisible random variable X. Our method uses the Lévy-Khintchine representation of the Laplace transform Ee-λX = e-ϕ(λ), where ϕ is the Laplace exponent. We apply the Post-Widder method for Laplace transform inversion combined with a sequence convergence accelerator to obtain accurate results. We demonstrate this technique on several examples, including the stable distribution, mixtures thereof, and integrals with respect to nonnegative Lévy processes.

A Generalized Approach on Outage Performance Analysis of Dual-Hop Decode and Forward Relaying for 5G and Beyond Scenarios

2021 ◽  
Author(s):  
Daljeet Singh
Keyword(s):  
Communication Systems ◽  
Cumulative Distribution Function ◽  
Signal To Noise Ratio ◽  
Cumulative Distribution ◽  
Wireless Communication Systems ◽  
Signal To Noise ◽  
Decode And Forward ◽  
Outage Performance ◽  
The Relationship ◽  
Universal Expression

Abstract This paper presents a generalized approach on performance of relay aided communication systems for 5G and beyond scenarios. A dual-hop decode and forwarding scheme is considered in the analysis. The relationship between the outage performance and cumulative distribution function (CDF) of signal to noise ratio (SNR) is exploited to derive a universal expression of outage probability valid for all fading scenarios irrespective of their nature or complexity. Further, an effort is made to parameterise the channel PDF in such a manner that reflects a commonly encountered practical fading scenario faced by current and future wireless communication systems. The analytical results obtained for various cases are validated by Monte-Carlo simulations.

DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

2001 ◽  
Vol 09 (01) ◽  
pp. 39-53 ◽  
Author(s):  
RONALD R. YAGER
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Cumulative Distribution ◽  
General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

Estimating the cumulative distribution function for the linear combination of gamma random variables

2017 ◽  
Vol 20 (5) ◽  
pp. 939-951
Author(s):  
Amal Almarwani ◽  
Bashair Aljohani ◽  
Rasha Almutairi ◽  
Nada Albalawi ◽  
Alya O. Al Mutairi
Keyword(s):  
Distribution Function ◽  
Linear Combination ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Cumulative Distribution

scholarly journals On the control of the difference between two Brownian motions: a dynamic copula approach

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Thomas Deschatre
Keyword(s):  
Cumulative Distribution Function ◽  
Survival Function ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Gaussian Copula ◽  
Brownian Motions ◽  
Dynamic Copula ◽  
Copula Approach ◽  
The Difference ◽  
The Right

AbstractWe propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. Our approach is based on the copula between the Brownian motion and its reflection. We show that the class of admissible copulae for the Brownian motions are not limited to the class of Gaussian copulae and that it also contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right tail than in the Gaussian copula case. Considering two Brownian motions B1t and B2t, the main result is that the range of possible values for is the same for Markovian pairs and all pairs of Brownian motions, that is with φ being the cumulative distribution function of a standard Gaussian random variable.

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