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We present a novel and accurate approximation for the distribution of the sum of equally correlated Nakagami-m variates. Ascertaining on this result we study the performance of Equal Gain Combining (EGC) receivers, operating over equally…

Information Theory · Computer Science 2009-08-26 Zoran Hadzi-Velkov , Nikola Zlatanov , George K. Karagiannidis

A probabilistic circuit (PC) succinctly expresses a function that represents a multivariate probability distribution and, given sufficient structural properties of the circuit, supports efficient probabilistic inference. Typically a PC…

Machine Learning · Computer Science 2024-08-09 Oliver Broadrick , William Cao , Benjie Wang , Martin Trapp , Guy Van den Broeck

We derive a fully analytical, one-line closed-form expression for the cumulative distribution function (CDF) of the product of two correlated zero-mean normal random variables, avoiding any series representation. This result complements the…

Probability · Mathematics 2025-09-15 Erdinc Akyildirim , Alper Hekimoglu

The sum of random variables (RVs) appears extensively in wireless communications, at large, both conventional and advanced, and has been subject of longstanding research. The statistical characterization of the referred sum is crucial to…

The one-point probability distribution function (PDF) of the matter density field in the universe is a fundamental property that plays an essential role in cosmology for estimates such as gravitational weak lensing, non-linear clustering,…

Cosmology and Nongalactic Astrophysics · Physics 2018-10-10 Anatoly Klypin , Francisco Prada , Juan Betancort-Rijo , Franco D. Albareti

Random matrix model for the Nakagami-q (Hoyt) fading in multiple-input multiple-output (MIMO) communication channels with arbitrary number of transmitting and receiving antennas is considered. The joint probability density for the…

Information Theory · Computer Science 2011-05-24 Santosh Kumar , Akhilesh Pandey

We report the similarity between the Nakagami-m fading distribution and the three Gaussian ensembles of random matrix theory. We provide a brief review of random matrix theory and wireless fading. We show that the Nakagami-m distribution…

Information Theory · Computer Science 2018-04-26 Sherif M. Abuelenin

We presents results of joint modeling of the probability distribution function (PDF) and the one-dimensional power spectrum (PS) of the Lya forest flux decrement. The sensitivity of these statistical measures to the shape and amplitude of…

Astrophysics · Physics 2009-11-10 Vincent Desjacques , Adi Nusser

This paper derives second-order statistics for diversity-combining techniques over Log-mu fading channels. Closed-form expressions for the level crossing rate (LCR) and average fading duration (AFD) are derived for pure selection combining…

Signal Processing · Electrical Eng. & Systems 2025-11-26 Godfred Kumi Tenkorang , Michel Daoud Yacoub

Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this work, we propose a solution to this problem by using a family of Rotation-based Iterative…

Machine Learning · Statistics 2016-02-02 Valero Laparra , Gustavo Camps-Valls , Jesús Malo

We present novel exact expressions and accurate closed-form approximations for the level crossing rate (LCR) and the average fade duration (AFD) of the double Nakagami-m random process. These results are then used to study the second order…

Information Theory · Computer Science 2009-08-26 Nikola Zlatanov , Zoran Hadzi-Velkov , George K. Karagiannidis

Learning the multivariate distribution of data is a core challenge in statistics and machine learning. Traditional methods aim for the probability density function (PDF) and are limited by the curse of dimensionality. Modern neural methods…

Machine Learning · Statistics 2022-10-14 Magda Amiridi , Nicholas D. Sidiropoulos

By means of the multifractal analysis (MFA), the expressions of the probability density functions (PDFs) are unified in a compact analytical formula which is valid for various quantities in turbulence. It is shown that the formula can…

Statistical Mechanics · Physics 2009-11-10 Toshihico Arimitsu , Naoko Arimitsu

Decode-and-forward (DF) cooperative communication based on free space optical (FSO) links is studied in this letter. We analyze performance of the DF protocol in the FSO links following the Gamma-Gamma distribution. The cumulative…

Information Theory · Computer Science 2015-06-05 Manav R. Bhatnagar

We have discovered analytical expressions for the probability density function (PDF) of photons that are multiply scattered in relativistic flows, under the assumption of isotropic and inelastic scattering. These expressions characterize…

Prior asymptotic performance analyses are based on the series expansion of the moment-generating function (MGF) or the probability density function (PDF) of channel coefficients. However, these techniques fail for lognormal fading channels…

Information Theory · Computer Science 2017-07-27 Bingcheng Zhu , Julian Cheng , Jun Yan , Jinyuan Wang , Lenan Wu , Yongjin Wang

Chaotic Communications have drawn a great deal of attention to the wireless communication industry and research due to its limitless meritorious features, including excellent anti-fading and anti-intercept capabilities and jamming…

Information Theory · Computer Science 2016-08-02 Ehab Salahat

Time series analysis allows for the determination of the Power Spectral Density (PSD) and Probability Density Function (PDF) for astrophysical sources. The former of these illustrates the distribution of power at various timescales,…

High Energy Astrophysical Phenomena · Physics 2019-09-04 Paul J. Morris , Nachiketa Chakraborty , Garret Cotter

Multimode/multicore fibers are expected to provide an attractive solution to overcome the capacity limit of the current optical communication system. In the presence of high cross-talk between modes/cores, the squared singular values of the…

Information Theory · Computer Science 2020-06-11 Amor Nafkha , Nizar Demni

A theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent plasma transport events in unforced zonal flows is provided within the Charney-Hasegawa-Mima (CHM) model. The governing equation is…

Plasma Physics · Physics 2015-05-13 Johan Anderson , Gert J. J. Botha
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