scholarly journals FUNCTIONS OF DISTRIBUTIONS OF AMOUNTS OF UNIFORALLY DISTRIBUTED RANDOM VALUES OF TIMES OF PROCESSING THE REQUEST OF THE INFOCOMMUNICATION SYSTEM

2020 ◽  
Vol 6 (334) ◽  
pp. 36-44
Author(s):  
M.Yu. Babich ◽  
◽  
M.M. Butaev ◽  
A.A. Tarasov ◽  
A.I. Ivanov ◽  
...  
Keyword(s):  
Normal Distribution ◽  
Initial Approximation ◽  
Random Variable ◽  
Sequential Processing ◽  
Processing Times ◽  
Distribution Laws ◽  
Request Processing ◽  
Object Of Study ◽  
Properties Of Information ◽  
Interval Distribution

The normal distribution of a random variable is usually used in studies of the probabilistic properties of information systems. Using the normal distribution to approximate the distributions determined over a bounded distorts the physical meaning of the model and the numerical results obtained can only be used as an initial approximation. The purpose of the work is to improve methods for calculating the probability properties of infocommunication systems. The object of study is an analytical method for calculating the request processing time in the system, the subject is the formula for calculating the duration of sequential processing of a request by elements of the system with uniformly distributed independent random processing times. For positive random variables, it is proposed to use finite-interval distribution laws, for example, beta distribution. Density formulas and probability functions for the sums of two, three, and four independent randomly distributed variables are given.

scholarly journals ANALYTICAL EVALUATION OF PROCESSING TIME OF A QUERY IN AN INFORMATION SYSTEM

2018 ◽  
pp. 69-73 ◽  
Author(s):  
M. M. Butaev ◽  
A. A. Tarasov
Keyword(s):  
Information Systems ◽  
Normal Distribution ◽  
Processing Time ◽  
Random Variables ◽  
Initial Approximation ◽  
Random Variable ◽  
Sequential Processing ◽  
Processing Times ◽  
Distribution Laws ◽  
Interval Distribution

The normal distribution of a random variable is usually used in studies of the probabilistic characteristics of information systems. However, the approximation by the normal distribution of distributions determined on a limited interval distorts the physical meaning of the model and the numerical results, and it can only be used as an initial approximation. The aim of the work is to improve the methods for calculating the probabilistic characteristics of information systems. The object of the study is an analytical method for calculating the processing time of the query in the system. The subject of the study are formulas for calculating the duration of sequential processing of the query by elements of the system with uniformly distributed random processing times. In deriving the formulas for calculating the probability characteristics of a sum of independent uniformly distributed random variables, the methods of the theory of probability and statistics are applied. It is proposed for random variables, determined only on the positive coordinate axis, to use finite-interval distribution laws, for example, beta distribution. Density formulas and probability functions for sums of two, three and four independent uniformly distributed random variables are derived.

scholarly journals Characteristics of distribution of amounts of several uniformly distributed random values of information system query treatment times

2019 ◽  
pp. 59-63
Author(s):  
M. M. Butaev
Keyword(s):  
Information Systems ◽  
Random Variables ◽  
Initial Approximation ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Sequential Processing ◽  
Processing Times ◽  
Distribution Laws ◽  
Positive Axis ◽  
Interval Distribution

The normal distribution of a random variable is usually used in studies of the probabilistic characteristics of information systems. However, its use to approximate distributions defined on a limited interval distorts the physical meaning of the model and the numerical results, so it can only be used as an initial approximation. The purpose of the work is the improvement of calculation methods the probabilistic characteristics of information systems. The object of the research is an analytical method for calculating the processing time of a query in the system, the subject is a formula for calculating the duration of a sequential processing of a query by system elements with uniformly distributed random processing times. When deriving formulas for calculating the probability characteristics of a sum of independent uniformly distributed random variables, methods of probability theory are used. For random variables determined only on the positive axis of coordinates, it is proposed to use finite-interval distribution laws, for example, beta distribution. Formulas probability density function and cumulative distribution function for sums of two, three, and four independent uniformly distributed random variables are derived.

scholarly journals ДОСЛІДЖЕННЯ ПОКАЗНИКА ЕФЕКТИВНОСТІ ЕКСПЛУАТАЦІЇ ЗАСОБІВ ВИМІРЮВАЛЬНОЇ ТЕХНІКИ МЕТОДОМ КОМПʼЮТЕРНОГО МОДЕЛЮВАННЯ

2020 ◽  
pp. 166-169
Author(s):  
Олександр Володимирович Томашевський ◽  
Геннадій Валентинович Сніжной
Keyword(s):  
Computer Simulation ◽  
Distribution Function ◽  
Normal Distribution ◽  
Failure Rate ◽  
Random Variable ◽  
Operational Efficiency ◽  
Distribution Law ◽  
Maintenance System ◽  
Wide Range ◽  
Calibration Interval

The operational efficiency of measuring equipment (ME) is important in determining the cost of maintaining ME. To characterize the operational efficiency of the ME, an efficiency indicator has been introduced, an increase of which will reduce costs caused by the release of defective products due to the use of ME with unreliable indications. Over time, the ME parameters change under the influence of external factors and the ME aging processes inevitably occur, as a result of which the parameters of the ME metrological service system change. Therefore, in the general case, the parameters of the metrological maintenance system of ME should be considered as random variables. Accordingly, the efficiency indicator of measuring instruments is also a random variable, for the determination of which it is advisable to apply the methods of mathematical statistics and computer simulation. The performance indicator depends on the parameters of the metrological maintenance ME system, such as the calibration interval, the time spent by the ME on metrological maintenance, and the likelihood of ME failure-free operation. As a random variable, the efficiency indicator has a certain distribution function. To determine the distribution function of the efficiency indicator and the corresponding statistical characteristics, a computer simulation method was used. A study was made of the influence on the indicator of the effectiveness of the parameters of the metrological maintenance system ME (interesting interval, the failure rate of ME). The value of the verification interval and the failure rate of MEs varied over a wide range typical of real production. The time spent by ME on metrological services is considered as a random variable with a normal distribution law. To obtain random numbers with a normal distribution law, the Box-Muller method is used. After modeling, the statistical processing of the obtained results was done. It is shown that in real production, the efficiency indicator has a normal distribution law and the value of the efficiency indicator with an increase in the calibration interval does not practically change.

Analysis of Segmentation Parameters Effect towards Parallel Processing Time on Fuzzy C Means Algorithm

2018 ◽  
Vol 1 (4) ◽  
pp. 99
Author(s):  
Cepi Ramdani ◽  
Indah Soesanti ◽  
Sunu Wibirama
Keyword(s):  
Parallel Processing ◽  
Processing Time ◽  
Color Image ◽  
Clustering Algorithms ◽  
Fuzzy C Means ◽  
Sequential Processing ◽  
Processing Times ◽  
Parameter Values ◽  
Fuzzy C Means Algorithm ◽  
Segmentation Parameters

Fuzzy C Means algorithm or FCM is one of many clustering algorithms that has better accuracy to solve problems related to segmentation. Its application is almost in every aspects of life and many disciplines of science. However, this algorithm has some shortcomings, one of them is the large amount of processing time consumption. This research conducted mainly to do an analysis about the effect of segmentation parameters towards processing time in sequential and parallel. The other goal is to reduce the processing time of segmentation process using parallel approach. Parallel processing applied on Nvidia GeForce GT540M GPU using CUDA v8.0 framework. The experiment conducted on natural RGB color image sized 256x256 and 512x512. The settings of segmentation parameter values were done as follows, weight in range (2-3), number of iteration (50-150), number of cluster (2-8), and error tolerance or epsilon (0.1 – 1e-06). The results obtained by this research as follows, parallel processing time is faster 4.5 times than sequential time with similarity level of image segmentations generated both of processing types is 100%. The influence of segmentation parameter values towards processing times in sequential and parallel can be concluded as follows, the greater value of weight parameter then the sequential processing time becomes short, however it has no effects on parallel processing time. For iteration and cluster parameters, the greater their values will make processing time consuming in sequential and parallel become large. Meanwhile the epsilon parameter has no effect or has an unpredictable tendency on both of processing time.

COMPARISON OF APPROXIMATIONS FOR COMPOUND POISSON PROCESSES

2015 ◽  
Vol 45 (3) ◽  
pp. 601-637 ◽  
Author(s):  
Raffaello Seri ◽  
Christine Choirat
Keyword(s):  
Random Variable ◽  
Cumulative Distribution ◽  
Claim Amount ◽  
Approximation Methods ◽  
Total Claim Amount ◽  
Aggregate Claim ◽  
Time Period ◽  
Total Claim ◽  
The Difference ◽  
Object Of Study

AbstractIn this paper, we compare the error in several approximation methods for the cumulative aggregate claim distribution customarily used in the collective model of insurance theory. In this model, it is usually supposed that a portfolio is at risk for a time period of length t. The occurrences of the claims are governed by a Poisson process of intensity μ so that the number of claims in [0,t] is a Poisson random variable with parameter λ = μ t. Each single claim is an independent replication of the random variable X, representing the claim severity. The aggregate claim or total claim amount process in [0,t] is represented by the random sum of N independent replications of X, whose cumulative distribution function (cdf) is the object of study. Due to its computational complexity, several approximation methods for this cdf have been proposed. In this paper, we consider 15 approximations put forward in the literature that only use information on the lower order moments of the involved distributions. For each approximation, we consider the difference between the true distribution and the approximating one and we propose to use expansions of this difference related to Edgeworth series to measure their accuracy as λ = μ t diverges to infinity. Using these expansions, several statements concerning the quality of approximations for the distribution of the aggregate claim process can find theoretical support. Other statements can be disproved on the same grounds. Finally, we investigate numerically the accuracy of the proposed formulas.

scholarly journals A refinement of normal approximation to Poisson binomial

2005 ◽  
Vol 2005 (5) ◽  
pp. 717-728 ◽  
Author(s):  
K. Neammanee
Keyword(s):  
Normal Distribution ◽  
Normal Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Standard Normal Distribution ◽  
Bernoulli Random Variables ◽  
Binomial Random Variable ◽  
Standard Normal ◽  
Correction Terms ◽  
Better Than

LetX1,X2,…,Xnbe independent Bernoulli random variables withP(Xj=1)=1−P(Xj=0)=pjand letSn:=X1+X2+⋯+Xn.Snis called a Poisson binomial random variable and it is well known that the distribution of a Poisson binomial random variable can be approximated by the standard normal distribution. In this paper, we use Taylor's formula to improve the approximation by adding some correction terms. Our result is better than before and is of order1/nin the casep1=p2=⋯=pn.

scholarly journals On a Class of Distributions Stable Under Random Summation

2012 ◽  
Vol 49 (02) ◽  
pp. 303-318 ◽  
Author(s):  
L. B. Klebanov ◽  
A. V. Kakosyan ◽  
S. T. Rachev ◽  
G. Temnov
Keyword(s):  
Normal Distribution ◽  
Generating Function ◽  
Chebyshev Polynomials ◽  
Generating Functions ◽  
Analytic Functions ◽  
Random Variable ◽  
Random Summation ◽  
The Stability ◽  
Rational Generating Functions ◽  
Family Of Distributions

We study a family of distributions that satisfy the stability-under-addition property, provided that the number ν of random variables in a sum is also a random variable. We call the corresponding property ν-stability and investigate the situation when the semigroup generated by the generating function of ν is commutative. Using results from the theory of iterations of analytic functions, we describe ν-stable distributions generated by summations with rational generating functions. A new case in this class of distributions arises when generating functions are linked with Chebyshev polynomials. The analogue of normal distribution corresponds to the hyperbolic secant distribution.

scholarly journals Austenite Grain Size Estimtion from Chord Lengths of Logarithmic-Normal Distribution

2017 ◽  
Vol 62 (4) ◽  
pp. 2015-2019
Author(s):  
H. Adrian ◽  
K. Wiencek
Keyword(s):  
Grain Size ◽  
Normal Distribution ◽  
Gamma Distribution ◽  
Interval Estimation ◽  
Random Variable ◽  
Point Estimation ◽  
Size Estimation ◽  
Present Contribution ◽  
Austenite Grain Size ◽  
The One

AbstractLinear section of grains in polyhedral material microstructure is a system of chords. The mean length of chords is the linear grain size of the microstructure. For the prior austenite grains of low alloy structural steels, the chord length is a random variable of gamma- or logarithmic-normal distribution. The statistical grain size estimation belongs to the quantitative metallographic problems. The so-called point estimation is a well known procedure. The interval estimation (grain size confidence interval) for the gamma distribution was given elsewhere, but for the logarithmic-normal distribution is the subject of the present contribution. The statistical analysis is analogous to the one for the gamma distribution.

Uncertainty Analysis of Flood Forecasting in River Channel

2012 ◽  
Vol 550-553 ◽  
pp. 2489-2492
Author(s):  
Qun Hao ◽  
Ying Na Sun ◽  
Ning Jiang
Keyword(s):  
Uncertainty Analysis ◽  
Normal Distribution ◽  
Flood Control ◽  
Random Variable ◽  
Flood Forecasting ◽  
River Channel ◽  
Statistical Characteristics ◽  
Forecasting Model ◽  
Forward Algorithm ◽  
Linear Characteristic

In this paper, the stochastic differential equations theory was used to analyze the uncertainty of flood forecasting in river channel based on the forward algorithm of linear characteristic. And then a river channel flood forecasting model, in which the coefficient of storage and discharge was regarded as a random variable, was built. The statistical characteristics of outflow process could be taken part in theory by the built river channel flood forecasting model when the coefficient of storage obeyed a kind of normal distribution. Storage coefficient is random variable in the model. The results showed that the uncertainty degree of outflow process could be made through considering the uncertainty of river channel flood forecasting, which would provide some references for making decision in flood control.

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