On the Probability Densities of the Output of Some Random Systems

The influence on the approximation properties of a nonparametric probability density estimate of Rosenblatt-Parzen type of the information on the dependence of random variables is determined. The ratio of the asymptotic expressions of the mean square deviations of independent and dependent random variables is obtained. This relation for a two-dimensional random variable is considered as a quantitative assessment of the influence of information about their dependence on the approximation properties of the kernel probability density estimate. The established ratio is determined by the kind of probability density and the volumes of the initial statistical data that are used in estimating the probability densities of dependent and independent random variables. The general results obtained are considered in detail for two-dimensional linearly dependent random variables with normal distribution laws. The functional dependence of the ratio of the mean square deviations of the independent and dependent two-dimensional random variables on the correlation coefficient is determined. The dependence of the considered ratio on the volume of statistical data is analyzed. A method for estimating the functional of the second derivatives of two-dimensional random variables with normal distribution laws is developed. The results obtained are the basis for the development of modifications of “fast” procedures for optimizing kernel estimates of probability densities in conditions of large samples.

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Ensemble Mean Storm-Scale Performance in the Presence of Nonlinearity

Monthly Weather Review ◽

10.1175/mwr-d-14-00417.1 ◽

2015 ◽

Vol 143 (12) ◽

pp. 5115-5133 ◽

Cited By ~ 4

Author(s):

Michael A. Hollan ◽

Brian C. Ancell

Keyword(s):

Prediction Models ◽

Initial Conditions ◽

Weather Prediction ◽

Wrf Model ◽

Forecast Errors ◽

Ensemble Mean ◽

Deterministic Solution ◽

Significant Divergence ◽

The Mean ◽

And Control

Abstract The use of ensembles in numerical weather prediction models is becoming an increasingly effective method of forecasting. Many studies have shown that using the mean of an ensemble as a deterministic solution produces the most accurate forecasts. However, the mean will eventually lose its usefulness as a deterministic forecast in the presence of nonlinearity. At synoptic scales, this appears to occur between 12- and 24-h forecast time, and on storm scales it may occur significantly faster due to stronger nonlinearity. When this does occur, the question then becomes the following: Should the mean still be adhered to, or would a different approach produce better results? This paper will investigate the usefulness of the mean within a WRF Model utilizing an ensemble Kalman filter for severe convective events. To determine when the mean becomes unrealistic, the divergence of the mean of the ensemble (“mean”) and a deterministic forecast initialized from a set of mean initial conditions (“control”) are examined. It is found that significant divergence between the mean and control emerges no later than 6 h into a convective event. The mean and control are each compared to observations, with the control being more accurate for nearly all forecasts studied. For the case where the mean provides a better forecast than the control, an approach is offered to identify the member or group of members that is closest to the mean. Such a forecast will contain similar forecast errors as the mean, but unlike the mean, will be on an actual forecast trajectory.

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Statistical redundancy of instantaneous phases: theory and application to the seismic ambient wavefield

Geophysical Journal International ◽

10.1093/gji/ggv501 ◽

2015 ◽

Vol 204 (2) ◽

pp. 1159-1163 ◽

Cited By ~ 5

Author(s):

I. Gaudot ◽

É. Beucler ◽

A. Mocquet ◽

M. Schimmel ◽

M. Le Feuvre

Keyword(s):

Time Series ◽

Phase Coherence ◽

Pairwise Comparisons ◽

Gulf Of Guinea ◽

Source Characterization ◽

Second Moments ◽

Mean And Variance ◽

The Mean ◽

Seismic Wavefield ◽

Synchronous Time

Abstract In order to detect possible signal redundancies in the ambient seismic wavefield, we develop a new method based on pairwise comparisons among a set of synchronous time-series. This approach is based on instantaneous phase coherence statistics. The first and second moments of the pairwise phase coherence distribution are used to characterize the phase randomness. For perfect phase randomness, the theoretical values of the mean and variance are equal to 0 and $\sqrt{1-2/\pi }$, respectively. As a consequence, any deviation from these values indicates the presence of a redundant phase in the raw continuous signal. A previously detected microseismic source in the Gulf of Guinea is used to illustrate one of the possible ways of handling phase coherence statistics. The proposed approach allows us to properly localize this persistent source, and to quantify its contribution to the overall seismic ambient wavefield. The strength of the phase coherence statistics relies in its ability to quantify the redundancy of a given phase among a set of time-series with various useful applications in seismic noise-based studies (tomography and/or source characterization).

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A Comparison of Averaged and Full Models to Study the Third-Body Perturbation

The Scientific World JOURNAL ◽

10.1155/2013/136528 ◽

2013 ◽

Vol 2013 ◽

pp. 1-16 ◽

Cited By ~ 1

Author(s):

Carlos Renato Huaura Solórzano ◽

Antonio Fernando Bertachini de Almeida Prado

Keyword(s):

Initial Conditions ◽

Artificial Satellite ◽

Main Body ◽

Long Term Effects ◽

Third Body ◽

Mean Motion ◽

Short Period ◽

The Mean ◽

Averaged Models ◽

Averaged Model

The effects of a third-body travelling in a circular orbit around a main body on a massless satellite that is orbiting the same main body are studied under two averaged models, single and double, where expansions of the disturbing function are made, and the full restricted circular three-body problem. The goal is to compare the behavior of these two averaged models against the full problem for long-term effects, in order to have some knowledge of their differences. The single averaged model eliminates the terms due to the short period of the spacecraft. The double average is taken over the mean motion of the satellite and the mean motion of the disturbing body, so removing both short period terms. As an example of the methods, an artificial satellite around the Earth perturbed by the Moon is used. A detailed study of the effects of different initial conditions in the orbit of the spacecraft is made.

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Verification of a short-range ensemble precipitation prediction system over Iberia

Advances in Geosciences ◽

10.5194/adgeo-25-55-2010 ◽

2010 ◽

Vol 25 ◽

pp. 55-63 ◽

Cited By ~ 3

Author(s):

D. Santos-Muñoz ◽

M. L. Martin ◽

A. Morata ◽

F. Valero ◽

A. Pascual

Keyword(s):

Short Range ◽

Initial Conditions ◽

Ensemble Prediction ◽

Positive Contribution ◽

Prediction System ◽

Good Reliability ◽

Ensemble Prediction System ◽

Probabilistic Forecasts ◽

Ensemble Mean ◽

The Mean

Abstract. The purpose of this paper is the verification of a short-range ensemble prediction system (SREPS) built with five different model physical process parameterization schemes and two different initial conditions from global models, allowing to construct several versions of the non-hydrostatic mesoscale MM5 model for a 1-month period of October 2006. From the SREPS, flow-dependent probabilistic forecasts are provided by means of predictive probability distributions over the Iberian Peninsula down to 10-km grid spacing. In order to carry out the verification, 25 km grid of observational precipitation records over Spain from the Spanish Climatic Network has been used to evaluate the ensemble accuracy together with the mean model performance and forecast variability by means of comparisons between such records and the ensemble forecasts. This verification has been carried out upscaling the 10 km probabilistic forecast to the observational data grid. Temporal evolution of precipitation forecasts for spatial averaged ensemble members and the ensemble mean is shown, illustrating the consistency of the SREPS. Such evolutions summarize the SREPS information, showing each of the members as well as the ensemble mean evolutions. The Talagrand diagram derived from the SREPS results shows underdispersion which indicates some bias behaviour. The Relative Operating Characteristic (ROC) curve shows a very outstanding area, indicating potential usefulness of the forecasting system. The forecast probability and the mean observed frequency present good agreement with the SREPS results close to the no-skill line. Because the probability has a good reliability and a positive contribution to the brier skill score, a positive value of this skill is obtained. Moreover, the probabilistic meteogram of the spatial daily mean precipitation values shows the range of forecast values, providing discrete probability information in different quantile intervals. The epsgram shows different daily distributions, indicating the predictability of each day.

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the effects of resonance with Jupiter in the system of short-period comets

International Astronomical Union Colloquium ◽

10.1017/s0252921100033959 ◽

1974 ◽

Vol 22 ◽

pp. 193-203

Author(s):

L̆ubor Kresák

Keyword(s):

Structural Effects ◽

Order Resonance ◽

Mean Motion ◽

Short Period ◽

The Mean ◽

Compound Effect ◽

Low Order

AbstractStructural effects of the resonance with the mean motion of Jupiter on the system of short-period comets are discussed. The distribution of mean motions, determined from sets of consecutive perihelion passages of all known periodic comets, reveals a number of gaps associated with low-order resonance; most pronounced are those corresponding to the simplest commensurabilities of 5/2, 2/1, 5/3, 3/2, 1/1 and 1/2. The formation of the gaps is explained by a compound effect of five possible types of behaviour of the comets set into an approximate resonance, ranging from quick passages through the gap to temporary librations avoiding closer approaches to Jupiter. In addition to the comets of almost asteroidal appearance, librating with small amplitudes around the lower resonance ratios (Marsden, 1970b), there is an interesting group of faint diffuse comets librating in characteristic periods of about 200 years, with large amplitudes of about±8% in μ and almost±180° in σ, around the 2/1 resonance gap. This transient type of motion appears to be nearly as frequent as a circulating motion with period of revolution of less than one half that of Jupiter. The temporary members of this group are characteristic not only by their appearance but also by rather peculiar discovery conditions.

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Understanding the CoVID-19 pandemic Curve through statistical approach (Preprint)

10.2196/preprints.22675 ◽

2020 ◽

Author(s):

Ibrar Ul Hassan Akhtar

Keyword(s):

Probability Density ◽

Change Point ◽

Statistical Approach ◽

Sudden Change ◽

Global Scale ◽

Change Point Detection ◽

Segment Length ◽

Infected Population ◽

The Mean ◽

Point Detection

UNSTRUCTURED Current research is an attempt to understand the CoVID-19 pandemic curve through statistical approach of probability density function with associated skewness and kurtosis measures, change point detection and polynomial fitting to estimate infected population along with 30 days projection. The pandemic curve has been explored for above average affected countries, six regions and global scale during 64 days of 22nd January to 24th March, 2020. The global cases infection as well as recovery rate curves remained in the ranged of 0 ‒ 9.89 and 0 ‒ 8.89%, respectively. The confirmed cases probability density curve is high positive skewed and leptokurtic with mean global infected daily population of 6620. The recovered cases showed bimodal positive skewed curve of leptokurtic type with daily recovery of 1708. The change point detection helped to understand the CoVID-19 curve in term of sudden change in term of mean or mean with variance. This pointed out disease curve is consist of three phases and last segment that varies in term of day lengths. The mean with variance based change detection is better in differentiating phases and associated segment length as compared to mean. Global infected population might rise in the range of 0.750 to 4.680 million by 24th April 2020, depending upon the pandemic curve progress beyond 24th March, 2020. Expected most affected countries will be USA, Italy, China, Spain, Germany, France, Switzerland, Iran and UK with at least infected population of over 0.100 million. Infected population polynomial projection errors remained in the range of -78.8 to 49.0%.

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Weighted statistical binary patterns for facial feature representation

Applied Intelligence ◽

10.1007/s10489-021-02477-1 ◽

2021 ◽

Author(s):

Hung Phuoc Truong ◽

Thanh Phuong Nguyen ◽

Yong-Guk Kim

Keyword(s):

Comprehensive Evaluation ◽

Facial Feature ◽

Input Image ◽

Feature Representation ◽

Illumination Variation ◽

Straight Line ◽

Mean And Variance ◽

The Mean ◽

Face Datasets ◽

Degraded Images

AbstractWe present a novel framework for efficient and robust facial feature representation based upon Local Binary Pattern (LBP), called Weighted Statistical Binary Pattern, wherein the descriptors utilize the straight-line topology along with different directions. The input image is initially divided into mean and variance moments. A new variance moment, which contains distinctive facial features, is prepared by extracting root k-th. Then, when Sign and Magnitude components along four different directions using the mean moment are constructed, a weighting approach according to the new variance is applied to each component. Finally, the weighted histograms of Sign and Magnitude components are concatenated to build a novel histogram of Complementary LBP along with different directions. A comprehensive evaluation using six public face datasets suggests that the present framework outperforms the state-of-the-art methods and achieves 98.51% for ORL, 98.72% for YALE, 98.83% for Caltech, 99.52% for AR, 94.78% for FERET, and 99.07% for KDEF in terms of accuracy, respectively. The influence of color spaces and the issue of degraded images are also analyzed with our descriptors. Such a result with theoretical underpinning confirms that our descriptors are robust against noise, illumination variation, diverse facial expressions, and head poses.

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Groups and Individuals: Optical Flow Patterns of Broiler Chicken Flocks Are Correlated with the Behavior of Individual Birds

Animals ◽

10.3390/ani11020568 ◽

2021 ◽

Vol 11 (2) ◽

pp. 568

Author(s):

Sabine G. Gebhardt-Henrich ◽

Ariane Stratmann ◽

Marian Stamp Dawkins

Keyword(s):

Optical Flow ◽

Broiler Chicken ◽

Average Length ◽

Flow Patterns ◽

Group Level ◽

Positive Correlation ◽

Water Test ◽

Mean And Variance ◽

The Mean

Group level measures of welfare flocks have been criticized on the grounds that they give only average measures and overlook the welfare of individual animals. However, we here show that the group-level optical flow patterns made by broiler flocks can be used to deliver information not just about the flock averages but also about the proportion of individuals in different movement categories. Mean optical flow provides information about the average movement of the whole flock while the variance, skew and kurtosis quantify the variation between individuals. We correlated flock optical flow patterns with the behavior and welfare of a sample of 16 birds per flock in two runway tests and a water (latency-to-lie) test. In the runway tests, there was a positive correlation between the average time taken to complete the runway and the skew and kurtosis of optical flow on day 28 of flock life (on average slow individuals came from flocks with a high skew and kurtosis). In the water test, there was a positive correlation between the average length of time the birds remained standing and the mean and variance of flock optical flow (on average, the most mobile individuals came from flocks with the highest mean). Patterns at the flock level thus contain valuable information about the activity of different proportions of the individuals within a flock.

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A New Model for the Stochastic Point Reactor: Development and Comparison with Available Models

Energies ◽

10.3390/en14040955 ◽

2021 ◽

Vol 14 (4) ◽

pp. 955

Author(s):

Alamir Elsayed ◽

Mohamed El-Beltagy ◽

Amnah Al-Juhani ◽

Shorooq Al-Qahtani

Keyword(s):

Kinetic Model ◽

Differential Equations ◽

Test Cases ◽

System Of Differential Equations ◽

Reactor Model ◽

Time System ◽

New Model ◽

Reactor Dynamics ◽

Mean And Variance ◽

The Mean

The point kinetic model is a system of differential equations that enables analysis of reactor dynamics without the need to solve coupled space-time system of partial differential equations (PDEs). The random variations, especially during the startup and shutdown, may become severe and hence should be accounted for in the reactor model. There are two well-known stochastic models for the point reactor that can be used to estimate the mean and variance of the neutron and precursor populations. In this paper, we reintroduce a new stochastic model for the point reactor, which we named the Langevin point kinetic model (LPK). The new LPK model combines the advantages, accuracy, and efficiency of the available models. The derivation of the LPK model is outlined in detail, and many test cases are analyzed to investigate the new model compared with the results in the literature.

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