Inaccuracies of Measuring Methods and Their Influence on the Regression Function

The quality parameters of electronic components and devices usually depend on the parameters of the materials. In many cases one does not know the theoretical relationship between the parameters, and therefore one makes technological experiments and measures the values of the parameters. Usually it is necessary to take several measuring points and calculate from this the unknown relationship between the parameters.The simplest equation that one can use is the linear function. In this case the theoretical probability density function is a Gaussian-function. Otherwise it is necessary to assume that the linear function is an approximation.When the measuring process has an inaccuracy, then one can show that the increase of the linear function is smaller and it is necessary to estimate a factor of correction to calculate the theoretical or exact relationship.

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ESTIMATION OF QUALITY PARAMETERS IN THE RADIO FLIGHT SUPPORT OPERATIONAL SYSTEM

Aviation ◽

10.3846/16487788.2016.1227541 ◽

2016 ◽

Vol 20 (3) ◽

pp. 123-128 ◽

Cited By ~ 11

Author(s):

Oleksandr SOLOMENTSEV ◽

Maksym ZALISKYI ◽

Oleksiy ZUIEV

Keyword(s):

Probability Density Function ◽

Probability Density ◽

Density Function ◽

Finite Time ◽

Quality Parameters ◽

Time Interval ◽

Finite Time Interval ◽

Operational System ◽

Radio Equipment ◽

Probability Density Function Pdf

The paper considers the structure of the operational system of radio equipment, determines the procedures related to the estimation of the quality parameters in the radio flight support operational system, using the ready-to-operate factor and the probability of no failure operation in a finite time interval, and shows the analytical ratios for the probability density function (PDF).

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Partial Histogram Bayes Learning Algorithm for Classification Applications

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i4.11.20787 ◽

2018 ◽

Vol 7 (4.11) ◽

pp. 126

Author(s):

Haider O. Lawend ◽

Anuar M. Muad ◽

Aini Hussain

Keyword(s):

Probability Density Function ◽

Probability Density ◽

Density Function ◽

Learning Algorithm ◽

Gaussian Function ◽

Real Data ◽

Distribution Functions ◽

Factors Affecting ◽

Probability Distribution Functions ◽

Large Memory

This paper presents a proposed supervised classification technique namely partial histogram Bayes (PHBayes) learning algorithm. Conventional classifier based on Gaussian function has limitation when dealing with different probability distribution functions and requires large memory for large number of instance. Alternatively, histogram based classifiers are flexible for different probability density function. The aims of PHBayes are to handle large number of instances in datasets with lesser memory requirement, and fast in training and testing phases. The PHBayes depends on portion of the observed histogram that is similar to the probability density function. PHBayes was analyzed using synthetic and real data. Several factors affecting classification accuracy were considered. The PHBayes was compared with other established classifiers and demonstrated higher accurate classification, lesser memory even when dealing with large number of instance, and faster in training and testing phases.

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The integrals and integral transformations connected with the joint vector Gaussian distribution

Proceedings of the National Academy of Sciences of Belarus Physics and Mathematics Series ◽

10.29235/1561-2430-2021-57-2-206-216 ◽

2021 ◽

Vol 57 (2) ◽

pp. 206-216

Author(s):

V. S. Mukha ◽

N. F. Kako

Keyword(s):

Probability Density Function ◽

Decision Theory ◽

Probability Density ◽

Density Function ◽

Regression Function ◽

Statistical Decision Theory ◽

Total Probability ◽

Statistical Decision ◽

Gaussian Probability Density Function ◽

Integral Transformations

In many applications it is desirable to consider not one random vector but a number of random vectors with the joint distribution. This paper is devoted to the integral and integral transformations connected with the joint vector Gaussian probability density function. Such integral and transformations arise in the statistical decision theory, particularly, in the dual control theory based on the statistical decision theory. One of the results represented in the paper is the integral of the joint Gaussian probability density function. The other results are the total probability formula and Bayes formula formulated in terms of the joint vector Gaussian probability density function. As an example the Bayesian estimations of the coefficients of the multiple regression function are obtained. The proposed integrals can be used as table integrals in various fields of research.

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