Statistical Analysis of Phase-Only Correlation Functions Between Two Signals with Stochastic Phase-Spectra Following Bivariate Circular Probability Distributions

2020 ◽  
Vol E103.A (2) ◽  
pp. 478-485
Author(s):  
Shunsuke YAMAKI ◽  
Ryo SUZUKI ◽  
Makoto YOSHIZAWA
Keyword(s):  
Statistical Analysis ◽  
Correlation Functions ◽  
Probability Distributions ◽  
Phase Spectra

scholarly journals Statistical Analysis and Machine Learning Prediction of Fog-Caused Low-Visibility Events at A-8 Motor-Road in Spain

Atmosphere ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 679
Author(s):  
Sara Cornejo-Bueno ◽  
David Casillas-Pérez ◽  
Laura Cornejo-Bueno ◽  
Mihaela I. Chidean ◽  
Antonio J. Caamaño ◽  
...  
Keyword(s):  
Statistical Analysis ◽  
Probability Distributions ◽  
Pearson Correlation ◽  
Likelihood Method ◽  
Neural Network Approach ◽  
Event Duration ◽  
Full Characterization ◽  
Low Visibility ◽  
Learning Machine ◽  
The Impact

This work presents a full statistical analysis and accurate prediction of low-visibility events due to fog, at the A-8 motor-road in Mondoñedo (Galicia, Spain). The present analysis covers two years of study, considering visibility time series and exogenous variables collected in the zone affected the most by extreme low-visibility events. This paper has then a two-fold objective: first, we carry out a statistical analysis for estimating the fittest probability distributions to the fog event duration, using the Maximum Likelihood method and an alternative method known as the L-moments method. This statistical study allows association of the low-visibility depth with the event duration, showing a clear relationship, which can be modeled with distributions for extremes such as Generalized Extreme Value and Generalized Pareto distributions. Second, we apply a neural network approach, trained by means of the ELM (Extreme Learning Machine) algorithm, to predict the occurrence of low-visibility events due to fog, from atmospheric predictive variables. This study provides a full characterization of fog events at this motor-road, in which orographic fog is predominant, causing important traffic problems during all year. We also show how the ELM approach is able to obtain highly accurate low-visibility events predictions, with a Pearson correlation coefficient of 0.8, within a half-hour time horizon, enough to initialize some protocols aiming at reducing the impact of these extreme events in the traffic of the A-8 motor road.

The ellipsoidal form of clasts with practical applications to fabric and size analyses of fluvial gravels

1980 ◽  
Vol 17 (12) ◽  
pp. 1725-1739 ◽  
Author(s):  
Emlyn H. Koster ◽  
Brian R. Rust ◽  
Don J. Gendzwill
Keyword(s):  
Statistical Analysis ◽  
Flow Direction ◽  
Probability Distributions ◽  
Size Analysis ◽  
Shape Variation ◽  
Practical Applications ◽  
Flow Interactions ◽  
Typical Range ◽  
Plane Area ◽  
Key Parameter

The widespread assumption that most water-worn gravel clasts approximate ellipsoids is confirmed by a statistical analysis of available data. The analysis demonstrates a Gaussian distribution of V/Ve ratios, centred on unit ratio, where V is clast volume and Ve the volume of a symmetric ellipsoid with equivalent triaxial dimensions. For internally isotropic and unbroken clasts, ellipsoidal form evolves as the rounding due to abrasion reaches its final stages. There appears to be no other major control on the tendency towards ellipsoidal geometry. The ellipsoidal tendency assists the interpretation of fluvial gravel deposits, which depends greatly on accurate description of clast size and fabric.Firstly, it facilitates calculation of Ap, the plane area projected upstream by clasts, a key parameter in bed–flow interactions such as preferred fabric. Formulae are derived to calculate Ap for ellipsoidal clasts with any configuration relative to flow direction. Viewing fabric in terms of the Ap variable supports and explains earlier conclusions concerning the controls on variability of imbrication angle.Secondly, an investigation of the relative merits of six size measures as descriptors of areal trends and predictors of nominal diameter, dn, concludes that (abc)1/3(the formula for dn of an ellipsoid) is superior. Other measures, namely, a, b, c, (a + c)/2, and (a + b + c)/3, are all subject to error in proportion to the degree of shape variation. Also, since downstream fining is typically accompanied by a changing proportion of oblate, bladed, prolate, and equant forms, dn is subject to inconsistent levels of under- or overestimation. The commonly used b dimension is endorsed as an acceptable predictor of dn, but a severely overestimates dn and should be abandoned. Information on errors in size analysis is presented as nomograms in the form of contoured c/b versus b/a plots and as probability distributions based on the typical range of shape variation in fluvial gravel.

scholarly journals Six-vertex Models and the GUE-corners Process

2018 ◽  
Vol 2020 (6) ◽  
pp. 1794-1881
Author(s):  
Evgeni Dimitrov
Keyword(s):  
Correlation Functions ◽  
Probability Distributions ◽  
Gibbs Measures ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Difference Operators ◽  
Vertex Model ◽  
Gaussian Unitary Ensemble ◽  
Vertex Models ◽  
Higher Spin

Abstract We consider a class of probability distributions on the six-vertex model, which originates from the higher spin vertex models of [13]. We define operators, inspired by the Macdonald difference operators, which extract various correlation functions, measuring the probability of observing different arrow configurations. For the class of models we consider, the correlation functions can be expressed in terms of multiple contour integrals, which are suitable for asymptotic analysis. For a particular choice of parameters we analyze the limit of the correlation functions through the steepest descent method. Combining this asymptotic statement with some new results about Gibbs measures on Gelfand–Tsetlin cones and patterns, we show that the asymptotic behavior of our six-vertex model near the boundary is described by the Gaussian Unitary Ensemble-corners process.

CP VIOLATION IN THE B SYSTEM—A STATISTICAL ANALYSIS

1990 ◽  
Vol 05 (05) ◽  
pp. 337-347
Author(s):  
DAVID LONDON
Keyword(s):  
Statistical Analysis ◽  
Cp Violation ◽  
Standard Model ◽  
Probability Distributions ◽  
New Physics ◽  
Hadronic Decay ◽  
System A ◽  
The Standard Model ◽  
Model Predictions ◽  
Cp Asymmetries

The standard model predictions for CP violating hadronic decay asymmetries are presented in the form of probability distributions. From these distributions, it can be easily seen what the most likely values of these quantities are, which measurements would clearly be signs of new physics, and which values of the CP asymmetries would most constrain the parameters of the standard model.

scholarly journals Statistical deprojection of galaxy pairs

2018 ◽  
Vol 614 ◽  
pp. A45 ◽  
Author(s):  
Laurent Nottale ◽  
Pierre Chamaraux
Keyword(s):  
Statistical Analysis ◽  
Probability Distribution ◽  
Physical Properties ◽  
Previous Analysis ◽  
Probability Distributions ◽  
Second Step ◽  
Line Of Sight ◽  
Mass Determination ◽  
Dynamical Parameters

Aims. The purpose of the present paper is to provide methods of statistical analysis of the physical properties of galaxy pairs. We perform this study to apply it later to catalogs of isolated pairs of galaxies, especially two new catalogs we recently constructed that contain ≈1000 and ≈13 000 pairs, respectively. We are particularly interested by the dynamics of those pairs, including the determination of their masses. Methods. We could not compute the dynamical parameters directly since the necessary data are incomplete. Indeed, we only have at our disposal one component of the intervelocity between the members, namely along the line of sight, and two components of their interdistance, i.e., the projection on the sky-plane. Moreover, we know only one point of each galaxy orbit. Hence we need statistical methods to find the probability distribution of 3D interdistances and 3D intervelocities from their projections; we designed those methods under the term deprojection. Results. We proceed in two steps to determine and use the deprojection methods. First we derive the probability distributions expected for the various relevant projected quantities, namely intervelocity vz, interdistance rp, their ratio, and the product $r_p v_z^2$, which is involved in mass determination. In a second step, we propose various methods of deprojection of those parameters based on the previous analysis. We start from a histogram of the projected data and we apply inversion formulae to obtain the deprojected distributions; lastly, we test the methods by numerical simulations, which also allow us to determine the uncertainties involved.

scholarly journals Estimation of Population Prevalence of COVID-19 Using Imperfect Tests

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1900
Author(s):  
Leonid Hanin
Keyword(s):  
Statistical Analysis ◽  
Upper Bound ◽  
Unbiased Estimator ◽  
Probability Distributions ◽  
Heterogeneous Population ◽  
Prevalence Studies ◽  
Population Prevalence ◽  
Statistical Assumptions ◽  
Testing Data ◽  
Asymptotically Unbiased Estimator

I formulate three basic biomedical/statistical assumptions that should ideally guide well-designed population prevalence studies of the present or past disease including COVID-19. On the basis of these assumptions alone, I compute several probability distributions required for statistical analysis of testing data collected from a sample of individuals drawn from a heterogeneous population. I also construct a consistent asymptotically unbiased estimator of the population prevalence of the disease or infection from the collected data and derive a simple upper bound for its variance. All the results are rigorously proved and valid for any test for COVID-19 or other disease provided that the sum of the test’s sensitivity and specificity is larger than 1. A few recommendations for the design of COVID-19 prevalence studies informed by the results of this work are formulated. The methodology developed in this article may prove applicable to diseases and conditions other than COVID-19 as well as in some non-epidemiological settings.

scholarly journals An Arc Furnace as a Source of Voltage Disturbances—A Statistical Evaluation of Propagation in the Supply Network

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1076 ◽  
Author(s):  
Ryszard Klempka
Keyword(s):  
Statistical Analysis ◽  
Power System ◽  
Firefly Algorithm ◽  
Statistical Evaluation ◽  
Probability Distributions ◽  
Supply Network ◽  
Arc Furnace ◽  
Large Source ◽  
Basic Parameters ◽  
Modified Firefly Algorithm

This article presents the results of measuring Pst indicators at three points of a power system supplying a large source of voltage disturbances—an arc furnace. Measurements were made at three voltage levels: 30, 110, and 400 kV. Recorded values of Pst at each point were subjected to statistical analysis, the probability distributions were adjusted to their histograms, and the nature of changes in the basic parameters of these distributions with the distance from the source of disturbances was indicated. The adjustments of the distributions were made using a modified firefly algorithm.

Sign in / Sign up

Export Citation Format

Share Document