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Cybernetics and programming
Reference:

Approximation of the distribution law of the sum of beta distributed random variables

Oleinikova Svetlana Aleksandrovna

Doctor of Technical Science

Associate Professor, Department of Automated and Computing Systems, Voronezh State Technical University

394026, Russia, g. Voronezh, Moskovskii prospekt, 14

s.a.oleynikova@gmail.com
Другие публикации этого автора
 

 

DOI:

10.7256/2306-4196.2015.6.17225

Review date:

08-12-2015


Publish date:

19-01-2016


Abstract: The subject of the research in this paper is the probability density function (PDF) of the random variable, which is the sum of a finite number of beta values. This law is widespread in the theory of probability and mathematical statistics, because using it can be described by a sufficiently large number of random events, if the value of the corresponding continuous random variable concentrated in a certain range. Since the required sum of beta values can not be expressed by any of the known laws, there is the problem of estimating its density distribution. The aim is to find such approximation for the PDF of the sum of beta-values that would have the least error. To achieve this goal computational experiment was conducted, in which for a given number of beta values the numerical value of the PDF with the approximation of the desired density were compared. As the approximations it were used the normal and the beta distributions. As a conclusion of the experimental analysis the results, indicating the appropriateness the approximation of the desired law with the help of the beta distribution, were obtained. As one of the fields of application of the results the project management problem with the random durations of works is considered. Here, the key issue is the evaluation of project implementation time, which, because of the specific subject area, can be described by the sum of the beta values.


Keywords: random value, beta distribution, density function, normal distribution, the sum of random variables, computational experiment, recursive algorithm, approximation, error, PERT
This article written in Russian. You can find full text of article in Russian here .

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