scholarly journals RSSI Probability Density Functions Comparison Using Jensen-Shannon Divergence and Pearson Distribution

Technologies ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 26
Author(s):  
Antonios Lionis ◽  
Konstantinos P. Peppas ◽  
Hector E. Nistazakis ◽  
Andreas Tsigopoulos
Keyword(s):  
Probability Density ◽  
Atmospheric Turbulence ◽  
Probability Distributions ◽  
Probability Density Functions ◽  
Index Structure ◽  
Optical Channel ◽  
Density Functions ◽  
Free Space Optical ◽  
Leibler Divergence ◽  
Jensen Shannon Divergence

The performance of a free-space optical (FSO) communications link suffers from the deleterious effects of weather conditions and atmospheric turbulence. In order to better estimate the reliability and availability of an FSO link, a suitable distribution needs to be employed. The accuracy of this model depends strongly on the atmospheric turbulence strength which causes the scintillation effect. To this end, a variety of probability density functions were utilized to model the optical channel according to the strength of the refractive index structure parameter. Although many theoretical models have shown satisfactory performance, in reality they can significantly differ. This work employs an information theoretic method, namely the so-called Jensen–Shannon divergence, a symmetrization of the Kullback–Leibler divergence, to measure the similarity between different probability distributions. In doing so, a large experimental dataset of received signal strength measurements from a real FSO link is utilized. Additionally, the Pearson family of continuous probability distributions is also employed to determine the best fit according to the mean, standard deviation, skewness and kurtosis of the modeled data.

Comparison of probability density functions for analyzing irradiance statistics due to atmospheric turbulence

2012 ◽  
Vol 51 (25) ◽  
pp. 5996 ◽  
Author(s):  
Jason R. W. Mclaren ◽  
John C. Thomas ◽  
Jessica L. Mackintosh ◽  
Kerry A. Mudge ◽  
Kenneth J. Grant ◽  
...  
Keyword(s):  
Probability Density ◽  
Atmospheric Turbulence ◽  
Probability Density Functions ◽  
Density Functions

A New Approach to Probability in Engineering Design and Optimization

1984 ◽  
Vol 106 (1) ◽  
pp. 5-10 ◽  
Author(s):  
J. N. Siddall
Keyword(s):  
Probability Density ◽  
Engineering Design ◽  
Probability Distributions ◽  
Probability Density Functions ◽  
Density Functions ◽  
New Approach ◽  
Design And Optimization ◽  
Evolutionary Technique ◽  
Probability And Statistics

The anomalous position of probability and statistics in both mathematics and engineering is discussed, showing that there is little consensus on concepts and methods. For application in engineering design, probability is defined as strictly subjective in nature. It is argued that the use of classical methods of statistics to generate probability density functions by estimating parameters for assumed theoretical distributions should be used with caution, and that the use of confidence limits is not really meaningful in a design context. Preferred methods are described, and a new evolutionary technique for developing probability distributions of new random variables is proposed. Although Bayesian methods are commonly considered to be subjective, it is argued that, in the engineering sense, they are really not. A general formulation of the probabilistic optimization problem is described, including the role of subjective probability density functions.

scholarly journals Skewed Jensen—Fisher Divergence and Its Bounds

Foundations ◽  
2021 ◽  
Vol 1 (2) ◽  
pp. 256-264
Author(s):  
Takuya Yamano
Keyword(s):  
Probability Density ◽  
Fisher Information ◽  
Sobolev Inequality ◽  
Logarithmic Sobolev Inequality ◽  
Probability Density Functions ◽  
Density Functions ◽  
De Bruijn ◽  
Measure Of Similarity ◽  
Jensen Shannon Divergence ◽  
Variational Distance

A non-uniform (skewed) mixture of probability density functions occurs in various disciplines. One needs a measure of similarity to the respective constituents and its bounds. We introduce a skewed Jensen–Fisher divergence based on relative Fisher information, and provide some bounds in terms of the skewed Jensen–Shannon divergence and of the variational distance. The defined measure coincides with the definition from the skewed Jensen–Shannon divergence via the de Bruijn identity. Our results follow from applying the logarithmic Sobolev inequality and Poincaré inequality.

scholarly journals Exact and Approximate Weighted Model Integration with Probability Density Functions Using Knowledge Compilation

2019 ◽  
Vol 33 ◽  
pp. 7825-7833 ◽  
Author(s):  
Pedro Zuidberg Dos Martires ◽  
Anton Dries ◽  
Luc De Raedt
Keyword(s):  
Probability Density ◽  
Probabilistic Reasoning ◽  
Probability Distributions ◽  
Probability Density Functions ◽  
Knowledge Compilation ◽  
Model Integration ◽  
Weight Functions ◽  
Density Functions ◽  
Model Counting ◽  
Weighted Model

Weighted model counting has recently been extended to weighted model integration, which can be used to solve hybrid probabilistic reasoning problems. Such problems involve both discrete and continuous probability distributions. We show how standard knowledge compilation techniques (to SDDs and d-DNNFs) apply to weighted model integration, and use it in two novel solvers, one exact and one approximate solver. Furthermore, we extend the class of employable weight functions to actual probability density functions instead of mere polynomial weight functions.

The Estimation of Wind Speed and Wind Power Characteristics in Taiwan

2014 ◽  
Vol 535 ◽  
pp. 145-148
Author(s):  
Jeeng Min Ling ◽  
Kunkerati Lublertlop
Keyword(s):  
Wind Speed ◽  
Probability Density ◽  
Wind Power ◽  
Probability Distributions ◽  
Weibull Model ◽  
Probability Density Functions ◽  
Density Functions ◽  
Power Characteristics ◽  
Wind Characteristic ◽  
Better Than

In this paper, the Weibull, Gamma, Lognormal, Rayleigh probability density functions (PDF) were used to statistically analyze the characteristics of wind speed and evaluate the energy based on hourly records from years of 2004 to 2009 at 24 locations in Taiwan. Weibull model shows the best goodness probability density function for estimating behavior of wind characteristic within six years at 7 sites of weather station better than using the Gamma and Rayleigh model. The annual mean wind power density is estimated and compared by different index. The feasibility of probability distributions at different locations were investigated.

Probability Density Functions

2019 ◽  
pp. 108-130
Author(s):  
Therese M. Donovan ◽  
Ruth M. Mickey
Keyword(s):  
Bayesian Inference ◽  
Probability Distribution ◽  
Probability Density ◽  
Probability Distributions ◽  
Random Variable ◽  
Probability Density Functions ◽  
Density Functions ◽  
Normal Distributions ◽  
Likelihood Profile ◽  
Variable Probability

This chapter builds on probability distributions. Its focus is on general concepts associated with probability density functions (pdf’s), which are distributions associated with continuous random variables. The continuous uniform and normal distributions are highlighted as examples of pdf’s. These and other pdf’s can be used to specify prior distributions, likelihoods, and/or posterior distributions in Bayesian inference. Although this chapter specifically focuses on the continuous uniform and normal distributions, the concepts discussed in this chapter will apply to other continuous probability distributions. By the end of the chapter, the reader should be able to define and use the following terms for a continuous random variable: random variable, probability distribution, parameter, probability density, likelihood, and likelihood profile.

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