Product of κ-μ and α-μ Distributions and Their Composite Fading Distributions

Cumulative Distribution ◽

Total Power ◽

The Novel ◽

Mathematical Software ◽

Composite Fading ◽

Software Packages ◽

Study Product ◽

Close Form ◽

In this study, product of two independent and non-identically distributed (i.n.i.d.) random variables (RVs) for κ-μ fading distribution and α-μ fading distribution is considered. The novel exact series formulas for the product of two i.n.i.d. fading distributions κ-μ and α-μ are derived instead of Fox H-function to solve the problem that Fox H function with multiple RVs cannot be implemented in professional mathematical software packages as MATHEMATICA and MAPLE. Exact close-form expressions of probability density function (PDF) and cumulative distribution function (CDF) are deduced to represent provided product expressions and generalized composite multipath shadowing models. At last, these analytical results are validated with Monte Carlo simulations, it shows that for provided κ-μ/α-μ model nonlinear parameter has more important influence than multipath component in PDF and CDF when the ratio between the total power of the dominant components and<br>the total power of the scattered waves is same. <br>

Bin-Free Fitting of Probability Distributions Emphasizing DNA Histograms

10.1101/218933 ◽

2017 ◽

Author(s):

Nash Rochman

Keyword(s):

Probability Distributions ◽

Cumulative Distribution ◽

Data Set ◽

Cell Synchronization ◽

Approximate Probability ◽

A Cell ◽

The Right ◽

Probability Density Function Pdf ◽

Dna Histograms

AbstractIt is often challenging to find the right bin size when constructing a histogram to represent a noisy experimental data set. This problem is frequently faced when assessing whether a cell synchronization experiment was successful or not. In this case the goal is to determine whether the DNA content is best represented by a unimodal, indicating successful synchronization, or bimodal, indicating unsuccessful synchronization, distribution. This choice of bin size can greatly affect the interpretation of the results; however, it can be avoided by fitting the data to a cumulative distribution function (CDF). Fitting data to a CDF removes the need for bin size selection. The sorted data can also be used to reconstruct an approximate probability density function (PDF) without selecting a bin size. A simple CDF-based approach is presented and the benefits and drawbacks relative to usual methods are discussed.

Performance of Dual-Hop Relaying Over Shadowed Ricean Fading Channels

Journal of Electrical Engineering ◽

10.2478/v10187-011-0039-6 ◽

2011 ◽

Vol 62 (4) ◽

pp. 244-248 ◽

Cited By ~ 14

Author(s):

Aleksandra Cvetković ◽

Jelena Anastasov ◽

Stefan Panić ◽

Mihajlo Stefanović ◽

Dejan Milić

Keyword(s):

Lower Bound ◽

Fading Channels ◽

Numerical Results ◽

Cumulative Distribution ◽

Performance Gain ◽

Channel State ◽

Ricean Fading ◽

Average Bit Error Probability ◽

Performance of Dual-Hop Relaying Over Shadowed Ricean Fading Channels In this paper, an analytical approach for evaluating performance of dual-hop cooperative link over shadowed Ricean fading channels is presented. New lower bound expressions for the probability density function (PDF), cumulative distribution function (CDF) and average bit error probability (ABEP) for system with channel state information (CSI) relay are derived. Some numerical results are presented to show behavior of performance gain for the proposed system. Analytical exact and lower bound expression for the outage probability (OP) of CSI assisted relay are obtained and required numerical results are compared.

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

Mathematical Problems in Engineering ◽

10.1155/2013/147106 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6 ◽

Cited By ~ 4

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 ◽

Wireless Communication Systems ◽

Multihop Wireless ◽

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.

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

Materials Science Forum ◽

10.4028/www.scientific.net/msf.925.98 ◽

2018 ◽

Vol 925 ◽

pp. 98-103

Author(s):

Andriy A. Burbelko ◽

Daniel Gurgul ◽

Edward Guzik ◽

Wojciech Kapturkiewicz

Keyword(s):

Distribution Function ◽

Cross Section ◽

Length Distribution ◽

Cumulative Distribution ◽

Nucleation Kinetics ◽

Distribution Law ◽

Chord Length Distribution ◽

Random Sections ◽

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.

Probability Function Estimation of Rock Random Variables Using Chebyshev Orthogonal Polynomial

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.351-352.1673 ◽

2013 ◽

Vol 351-352 ◽

pp. 1673-1676

Author(s):

Feng Qiang Gong ◽

Shang Qian Hou ◽

Ting Yu Wu

Keyword(s):

Orthogonal Polynomial ◽

Probability Function ◽

Hard Rock ◽

Cumulative Distribution ◽

Function Estimation ◽

Chebyshev Orthogonal Polynomial ◽

Relative Errors ◽

Stochastic Reliability ◽

The Chebyshev orthogonal polynomial with sample moments (the origin moments) were used to approximate the probability density function (PDF) or cumulative distribution function (CDF) of variable (CPA method). Three examples from observed datas of uniaxial compressive strength of a kind of hard rock were presented for illustrative purposes. The results show the PDF or CDF of rock variables can be accurately derived from CPA method with sample moments. The relative errors of estimation by CPA method is much smaller than that of TDF method (PDF fitted by some standard theoretical distributions). It is suggested that the presented method can be used in stochastic reliability analysis of rock engineering.

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

ACM Transactions on Modeling and Computer Simulation ◽

10.1145/3462201 ◽

2021 ◽

Vol 31 (4) ◽

pp. 1-36

Author(s):

Ran Yang ◽

David Kent ◽

Daniel W. Apley ◽

Jeremy Staum ◽

David Ruppert

Keyword(s):

Conditional Expectation ◽

Empirical Distribution ◽

Random Variables ◽

Cumulative Distribution ◽

Prior Work ◽

Density Deconvolution ◽

Computational Budget ◽

Naive Estimator ◽

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.

3-D Research about Walfisch-Bertoni Model

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.385-386.1527 ◽

2013 ◽

Vol 385-386 ◽

pp. 1527-1530 ◽

Cited By ~ 1

Author(s):

Jie Chen ◽

Dong Ya Shen ◽

Na Yao ◽

Ren Zhang

Keyword(s):

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.

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

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2018/v1i424552 ◽

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 ◽

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.

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

10.14293/s2199-1006.1.sor-.ppgnsjo.v1 ◽

2019 ◽

Author(s):

Oleg Gradov ◽

Eugene Adamovich ◽

Serge Pankratov

Keyword(s):

Distribution Function ◽

Probability Density Function ◽

Probability Density ◽

Density Function ◽

Cumulative Distribution ◽

Spectral Entropy ◽

Masking Noise ◽

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: