scholarly journals Functional inequalities for weighted Gamma distribution on the space of finite measures

2020 ◽  
Vol 25 (0) ◽  
Author(s):  
Feng-Yu Wang
Keyword(s):  
Gamma Distribution ◽  
Functional Inequalities ◽  
Finite Measures

STRUCTURAL CONNECTIONS AND INTERCHANGEABILITY OF ASYMMETRIC TYPES OF THEORETICAL DISTRIBUTIONS

2020 ◽  
Vol 6 (8(77)) ◽  
pp. 13-17
Author(s):  
Azimkhan Kurmankozhayev ◽  
Elmira Seilbekovna Yesbergenova
Keyword(s):  
Weibull Distribution ◽  
Empirical Analysis ◽  
Gamma Distribution ◽  
Statistical Data ◽  
Distribution Patterns ◽  
Structural Relationships ◽  
Statistical Regularities ◽  
Structural Connections ◽  
Characteristic Features ◽  
Structural Connection

Presented the results of evaluation of structural connection, identity and interchangeability of main asymmetric types of theoretical distributions most often acceptable for assessing the distributions of various indicators in geology and technology. The method of empirical analysis and statistical inference was used with the involvement of nonparametric facts according to the distribution patterns. The analysis of the empirical results of the application of the lognormal, gamma distribution and the Weibull distribution with the involvement of extensive statistical data from literary and research sources is carried out. The characteristic features and statistical regularities of distributions inherent to them are revealed, estimated statistical conclusions are obtained, according to which structural relationships between the functions of the lognormal, gamma and Weibull distributions are revealed. The identity and authenticity of the development of probabilistic frequencies in their application have been established, the complex geometric "image" of asymmetry inherent to these types of distributions is generalized. Structural relationships and interchangeability of asymmetric types of distributions are recommended to increase the reliability and credibility of the estimated choice of distribution in conditions of uncertainty and insignificance of statistical data when solving problems associated with forecasts, technological and computer developments.

Smoothing of stationary random signal in continuous flow mixer with gamma-distribution of residence times

1985 ◽  
Vol 50 (11) ◽  
pp. 2545-2557
Author(s):  
Pavel Hasal ◽  
Vladimír Kudrna ◽  
Jitka Vyhlídková
Keyword(s):  
Theoretical Analysis ◽  
Gamma Distribution ◽  
Continuous Flow ◽  
Random Signal ◽  
Linear Filter ◽  
Residence Times ◽  
Statistical Parameters ◽  
Basic Parameters

The paper is focused on a theoretical analysis of the function of continuous flow mixer with the so-called gamma-distribution of fluid residence times, used as a linear filter smoothing undesirable fluctuations of input properties. A relation is derived expressing the degree of smoothing of the signal passing through the system, as a function of statistical parameters of this signal and of gamma-distribution of fluid-residence times in the mixer. The analysis of this relation leads to conclusions concerning the prediction of the operation of smoothing mixers or the design of their basic parameters.

scholarly journals Functional Inequalities for Two-Level Concentration

2021 ◽  
Author(s):  
Franck Barthe ◽  
Michał Strzelecki
Keyword(s):  
Sobolev Inequality ◽  
Poincaré Inequality ◽  
Logarithmic Sobolev Inequality ◽  
Probability Measures ◽  
Exponential Rate ◽  
Functional Inequalities ◽  
Concentration Inequality ◽  
Poincare Inequality ◽  
Free Concentration ◽  
Concentration Property

AbstractProbability measures satisfying a Poincaré inequality are known to enjoy a dimension-free concentration inequality with exponential rate. A celebrated result of Bobkov and Ledoux shows that a Poincaré inequality automatically implies a modified logarithmic Sobolev inequality. As a consequence the Poincaré inequality ensures a stronger dimension-free concentration property, known as two-level concentration. We show that a similar phenomenon occurs for the Latała–Oleszkiewicz inequalities, which were devised to uncover dimension-free concentration with rate between exponential and Gaussian. Motivated by the search for counterexamples to related questions, we also develop analytic techniques to study functional inequalities for probability measures on the line with wild potentials.

An investigation of 16-QAM signal transmission over turbulent RoFSO link modeled by gamma–gamma distribution

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Abhishek Tripathi ◽  
Shilpi Gupta ◽  
Abhilash Mandloi ◽  
Gireesh G Soni
Keyword(s):  
Gamma Distribution ◽  
Free Space ◽  
Signal Transmission ◽  
Channel Modeling ◽  
Symbol Error Rate ◽  
Average Error ◽  
60 Ghz ◽  
Free Space Optical ◽  
Error Vector Magnitude ◽  
Space Optical Communication

AbstractThis paper outlines the performance of a 10 Gbit/s rectangular 16-quadrature amplitude modulation–based radio over free space optical communication system. Here, 60 GHz radio frequency–modulated signal is propagated through a 1550-nm free space optical link. The gamma–gamma distribution is used for the channel modeling of weak to strong atmospheric turbulence. The reported constellation plots and eye patterns are attributed to impairment factors in adverse conditions of atmosphere. The evaluation is carried out that the variation in average error vector magnitude in the range of 1.45–1.63% and equivalent symbol error rate of 0.019–0.023 are obtained for a clear atmosphere compared to the turbulent link of 0.2–1 km, respectively.

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