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 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 On the Properties and Applications of Transmuted Odd Generalized Exponential-Exponential Distribution

2018 ◽  
pp. 1-14
Author(s):  
Jamila Abdullahi ◽  
Umar Kabir Abdullahi ◽  
Terna Godfrey Ieren ◽  
David Adugh Kuhe ◽  
Adamu Abubakar Umar
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Exponential Distribution ◽  
Cumulative Distribution Function ◽  
Real Life ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Method Of Maximum Likelihood ◽  
Probability Density Function Pdf ◽  
New Distribution

This article proposed a new distribution referred to as the transmuted odd generalized exponential-exponential distribution (TOGEED) as an extension of the popular odd generalized exponential- exponential distribution by using the Quadratic rank transmutation map (QRTM) proposed and studied by [1]. Using the transmutation map, we defined the probability density function (pdf) and cumulative distribution function (cdf) of the transmuted odd generalized Exponential- Exponential distribution. Some properties of the new distribution were extensively studied after derivation. The estimation of the distribution’s parameters was also done using the method of maximum likelihood estimation. The performance of the proposed probability distribution was checked in comparison with some other generalizations of Exponential distribution using a real life dataset.  

scholarly journals Evolution of bioacoustic correlometers: from setups for analysis of probability density function (PDF), cumulative distribution function (CDF), [spectral] entropy of signal (SE) & quality of masking noise (QMN) to palmtop-like pocket devices

2019 ◽  
Author(s):  
Oleg Gradov ◽  
Eugene Adamovich ◽  
Serge Pankratov
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Spectral Entropy ◽  
Masking Noise ◽  
Probability Density Function Pdf

Evolution of bioacoustic correlometers: from setups for analysis of probability density function (PDF), cumulative distribution function (CDF), [spectral] entropy of signal (SE) & quality of masking noise (QMN) to palmtop-like pocket devices Novel references:

scholarly journals Moments of Distance from a Vertex to a Uniformly Distributed Random Point within Arbitrary Triangles

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Hongjun Li ◽  
Xing Qiu
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Standard Deviation ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Cumulative Distribution Function ◽  
Random Point ◽  
Cumulative Distribution ◽  
Computational Technique ◽  
Probability Density Function Pdf

We study the cumulative distribution function (CDF), probability density function (PDF), and moments of distance between a given vertex and a uniformly distributed random point within a triangle in this work. Based on a computational technique that helps us provide unified formulae of the CDF and PDF for this random distance then we compute its moments of arbitrary orders, based on which the variance and standard deviation can be easily derived. We conduct Monte Carlo simulations under various conditions to check the validity of our theoretical derivations. Our method can be adapted to study the random distances sampled from arbitrary polygons by decomposing them into triangles.

The joint asymptotic distribution of the k-smallest sample spacings

1969 ◽  
Vol 6 (02) ◽  
pp. 442-448
Author(s):  
Lionel Weiss
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Cumulative Distribution Function ◽  
Open Interval ◽  
Cumulative Distribution ◽  
The Right ◽  
Sample Spacings ◽  
Independent Identically Distributed

Suppose Q 1 ⋆, … Q n ⋆ are independent, identically distributed random variables, each with probability density function f(x), cumulative distribution function F(x), where F(1) – F(0) = 1, f(x) is continuous in the open interval (0, 1) and continuous on the right at x = 0 and on the left at x = 1, and there exists a positive C such that f(x) > C for all x in (0, l). f(0) is defined as f(0+), f(1) is defined as f(1–).

Empirical Analyses of Income: Finland (2009) and Australia (1967-1968)

2021 ◽  
pp. 35-53
Author(s):  
Johan Fellman
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Lorenz Curve ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Income Data ◽  
Difference Quotients ◽  
The Lorenz Curve

Analyses of income data are often based on assumptions concerning theoretical distributions. In this study, we apply statistical analyses, but ignore specific distribution models. The main income data sets considered in this study are taxable income in Finland (2009) and household income in Australia (1967-1968). Our intention is to compare statistical analyses performed without assumptions of the theoretical models with earlier results based on specific models. We have presented the central objects, probability density function, cumulative distribution function, the Lorenz curve, the derivative of the Lorenz curve, the Gini index and the Pietra index. The trapezium rule, Simpson´s rule, the regression model and the difference quotients yield comparable results for the Finnish data, but for the Australian data the differences are marked. For the Australian data, the discrepancies are caused by limited data. JEL classification numbers: D31, D63, E64. Keywords: Cumulative distribution function, Probability density function, Mean, quantiles, Lorenz curve, Gini coefficient, Pietra index, Robin Hood index, Trapezium rule, Simpson´s rule, Regression models, Difference quotients, Derivative of Lorenz curve

scholarly journals A NOTE CONCERNING THE DISTANCES OF UNIFORMLY DISTRIBUTED POINTS FROM THE CENTRE OF A RECTANGLE

2012 ◽  
Vol 87 (1) ◽  
pp. 115-119 ◽  
Author(s):  
ROBERT STEWART ◽  
HONG ZHANG
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Density Function ◽  
Cumulative Distribution Function ◽  
Average Distance ◽  
Cumulative Distribution

AbstractGiven a rectangle containing uniformly distributed random points, how far are the points from the rectangle’s centre? In this paper we provide closed-form expressions for the cumulative distribution function and probability density function that characterise the distance. An expression for the average distance to the centre of the rectangle is also provided.

scholarly journals Stereological Analysis of the Statistical Distribution of the Size of Graphite Nodules in DI

2018 ◽  
Vol 925 ◽  
pp. 98-103
Author(s):  
Andriy A. Burbelko ◽  
Daniel Gurgul ◽  
Edward Guzik ◽  
Wojciech Kapturkiewicz
Keyword(s):  
Distribution Function ◽  
Cross Section ◽  
Cumulative Distribution Function ◽  
Length Distribution ◽  
Cumulative Distribution ◽  
Nucleation Kinetics ◽  
Distribution Law ◽  
Chord Length Distribution ◽  
Random Sections ◽  
Probability Density Function Pdf

The estimate of a distribution law of the nodule diameters in a volume of cast iron provides information about the graphite nucleation kinetics, and also about the crystallization kinetics. This information is essential for building more accurate mathematical models of the alloy crystallization. The mapping of a Cumulative Distribution Function (CDF3) of radii for graphite nodules in ductile iron is presented on the base of a Probability Density Function (PDF1) of the chord length distribution for random sections of the sample at the planar cross-section.

3-D Research about Walfisch-Bertoni Model

2013 ◽  
Vol 385-386 ◽  
pp. 1527-1530 ◽  
Author(s):  
Jie Chen ◽  
Dong Ya Shen ◽  
Na Yao ◽  
Ren Zhang
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Path Loss ◽  
Signal Propagation ◽  
Loss Probability ◽  
Cumulative Distribution ◽  
Diffraction Loss ◽  
Wireless Signal ◽  
Probability Density Function Pdf ◽  
Signal Field

Walfisch - Bertoni model is used to predict the average signal field intensity of the main street. The model considers the path loss of the free space, diffraction loss along the path, and the influence of the height of the building. There are six City parameters in Walfisch - Bertoni model influence communication quality. In this paper, the researches about path loss and its characteristics is under the case of considering two city parameters at the same time. Facts have proved that this case is more close to the actual that the wireless signal propagation environment. This paper mainly researched the path loss, probability density function (PDF) and cumulative distribution function (CDF) of the path loss.

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