A cumulant approximation of a multidimensional probability distribution

2012 ◽  
Vol 57 (6) ◽  
pp. 577-587 ◽  
Author(s):  
L. V. Labunets ◽  
N. L. Lebedeva ◽  
M. Yu. Chizhov
Keyword(s):  
Probability Distribution ◽  
Multidimensional Probability

scholarly journals ROTATION MATRIX SAMPLING SCHEME FOR MULTIDIMENSIONAL PROBABILITY DISTRIBUTION TRANSFER

2016 ◽  
Vol III-7 ◽  
pp. 103-110
Author(s):  
P. Srestasathiern ◽  
S. Lawawirojwong ◽  
R. Suwantong ◽  
P Phuthong
Keyword(s):  
Probability Distribution ◽  
Orthogonal Matrix ◽  
Rotation Matrix ◽  
Sampling Scheme ◽  
Uniform Rotation ◽  
Householder Transformation ◽  
Orthogonal Matrices ◽  
Matrix Sampling ◽  
Paper Address ◽  
Multidimensional Probability

This paper address the problem of rotation matrix sampling used for multidimensional probability distribution transfer. The distribution transfer has many applications in remote sensing and image processing such as color adjustment for image mosaicing, image classification, and change detection. The sampling begins with generating a set of random orthogonal matrix samples by Householder transformation technique. The advantage of using the Householder transformation for generating the set of orthogonal matrices is the uniform distribution of the orthogonal matrix samples. The obtained orthogonal matrices are then converted to proper rotation matrices. The performance of using the proposed rotation matrix sampling scheme was tested against the uniform rotation angle sampling. The applications of the proposed method were also demonstrated using two applications i.e., image to image probability distribution transfer and data Gaussianization.

scholarly journals Statistical Signal Processing by Using the Higher-Order Correlation between Sound and Vibration and Its Application to Fault Detection of Rotational Machine

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Hisako Masuike ◽  
Akira Ikuta
Keyword(s):  
Signal Processing ◽  
Probability Distribution ◽  
Time Domain ◽  
Statistical Signal Processing ◽  
Higher Order ◽  
Orthogonal Expansion ◽  
Mutual Relationship ◽  
Diagnosis Method ◽  
Correlation Information ◽  
Multidimensional Probability

In this study, a stochastic diagnosis method based on the changing information of not only a linear correlation but also a higher-order nonlinear correlation is proposed in a form suitable for online signal processing in time domain by using a personal computer, especially in order to find minutely the mutual relationship between sound and vibration emitted from rotational machines. More specifically, a conditional probability hierarchically reflecting various types of correlation information is theoretically derived by introducing an expression on the multidimensional probability distribution in orthogonal expansion series form. The effectiveness of the proposed theory is experimentally confirmed by applying it to the observed data emitted from a rotational machine driven by an electric motor.

scholarly journals ROTATION MATRIX SAMPLING SCHEME FOR MULTIDIMENSIONAL PROBABILITY DISTRIBUTION TRANSFER

2016 ◽  
Vol III-7 ◽  
pp. 103-110
Author(s):  
P. Srestasathiern ◽  
S. Lawawirojwong ◽  
R. Suwantong ◽  
P Phuthong
Keyword(s):  
Probability Distribution ◽  
Orthogonal Matrix ◽  
Rotation Matrix ◽  
Sampling Scheme ◽  
Uniform Rotation ◽  
Householder Transformation ◽  
Orthogonal Matrices ◽  
Matrix Sampling ◽  
Paper Address ◽  
Multidimensional Probability

This paper address the problem of rotation matrix sampling used for multidimensional probability distribution transfer. The distribution transfer has many applications in remote sensing and image processing such as color adjustment for image mosaicing, image classification, and change detection. The sampling begins with generating a set of random orthogonal matrix samples by Householder transformation technique. The advantage of using the Householder transformation for generating the set of orthogonal matrices is the uniform distribution of the orthogonal matrix samples. The obtained orthogonal matrices are then converted to proper rotation matrices. The performance of using the proposed rotation matrix sampling scheme was tested against the uniform rotation angle sampling. The applications of the proposed method were also demonstrated using two applications i.e., image to image probability distribution transfer and data Gaussianization.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

Determination of the Probability Distribution of the Mean Sound Level

2010 ◽  
Vol 35 (4) ◽  
pp. 543-550 ◽  
Author(s):  
Wojciech Batko ◽  
Bartosz Przysucha
Keyword(s):  
Probability Distribution ◽  
Probability Distribution Function ◽  
Mean Value ◽  
Sound Level ◽  
Function Form ◽  
Noise Levels ◽  
Logarithmic Mean ◽  
The Mean ◽  
Estimation Of Uncertainty

AbstractAssessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random resultsL1;L2; : : : ;Lnof the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

Increase Power Efficientand Reliability of Electrosupply of Consumers of Low Power

GIS Business ◽  
2019 ◽  
Vol 14 (4) ◽  
pp. 42-52
Author(s):  
Sadullayev Nasillo Nematovich ◽  
Safarov Alisher Bekmurodovich ◽  
Nematov Shuhrat Nasilloyevich ◽  
Mamedov Rasul Akif- Ogli
Keyword(s):  
Wind Speed ◽  
Probability Distribution ◽  
Low Power ◽  
Electric Power ◽  
Energy Sources ◽  
Wind Flow ◽  
Wind Rose ◽  
Energy Potential ◽  
Wind Power Installation ◽  
Wind Energy Potential

This article assesses the wind speed data and wind energy potential in the Bukhara region of Uzbekistan. In article it is stated a principle construction "hybrid" a source of the electric power consisting from wind power installation with mechanical store of energy, the solar panel with аккумулятор in common working with an electric network. The speed and direction of the wind measured at a height of 10 m were analyzed by the Weibull probability distribution functionTo determine the direction of wind flow (wind rose), a graph in Matlab environment was constructed. The method of an estimation energy of efficiency of the objects eating from several energy sources is offered. It is proved efficiency of application of such source of the electric power low power consumers

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