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 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 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 On Distribution Characteristics of a Fuzzy Random Variable

2018 ◽  
Vol 47 (2) ◽  
pp. 53-67 ◽  
Author(s):  
Jalal Chachi
Keyword(s):  
Probability Theory ◽  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Distribution Characteristics ◽  
Fuzzy Random Variables ◽  
Fuzzy Random

In this paper, rst a new notion of fuzzy random variables is introduced. Then, usingclassical techniques in Probability Theory, some aspects and results associated to a randomvariable (including expectation, variance, covariance, correlation coecient, etc.) will beextended to this new environment. Furthermore, within this framework, we can use thetools of general Probability Theory to dene fuzzy cumulative distribution function of afuzzy random variable.

scholarly journals Finiteness of Record values and Alternative Asymptotic Theory of Records with Atom Endpoints

2020 ◽  
Vol 15 (3) ◽  
pp. 2371-2385
Author(s):  
Gane Samb Lo ◽  
Harouna Sangaré ◽  
Cherif Mamadou Moctar Traoré ◽  
Mohammad Ahsanullah
Keyword(s):  
Negative Binomial ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Random Variable ◽  
Record Values ◽  
Cumulative Distribution ◽  
Hitting Times ◽  
Record Times ◽  
Binomial Random Variable ◽  
Upper Record Values

Asymptotic theories on record values and times, including central limit theorems, make sense only if the sequence of records values (and of record times) is infinite. If not, such theories could not even be an option. In this paper, we give necessary and/or sufficient conditions for the finiteness of the number of records. We prove, for example for iid real valued random variable, that strong upper record values are finite if and only if the upper endpoint is finite and is an atom of the common cumulative distribution function. The only asymptotic study left to us concerns the infinite sequence of hitting times of that upper endpoints, which by the way, is the sequence of weak record times. The asymptotic characterizations are made using negative binomial random variables and the dimensional multinomial random variables. Asymptotic comparison in terms of consistency bounds and confidence intervals on the different sequences of hitting times are provided. The example of a binomial random variable is given.

scholarly journals RELIABILITY ANALYSIS OF RHS STEEL TRUSSES JOINTS BASED ON THE P-BOXES APPROACH

2021 ◽  
Vol 17 (1) ◽  
pp. 87-97
Author(s):  
Anastasia Soloveva ◽  
Sergey Solovev
Keyword(s):  
Reliability Analysis ◽  
Epistemic Uncertainty ◽  
Random Variables ◽  
Random Variable ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Interval Estimate ◽  
Structural Elements ◽  
Aleatory And Epistemic Uncertainty ◽  
Steel Trusses

Reliability is one of the main indicators of structural elements mechanical safety. The choice of stochastic models is an important task in reliability analysis for describing the variability of random variables with aleatory and epistemic uncertainty. The article proposes a method for the reliability analysis of RHS (rectangular hollow sections) steel truss joints based on p-boxes approach. The p-boxes consist of two boundary distribution functions that create an area of possible distribution functions of a random variable. The using of p-boxes make possible to model random variables without making unreasonable assumptions about the exact cumulative distribution functions (CDF) or the exact values of the CDF parameters. The developed approach allows to give an interval estimate of the non-failure probability of the truss joints, which is necessary for a comprehensive (system) reliability analysis of the entire truss.

scholarly journals Statistical Analysis of Ratio of Random Variables and Its Application in Performance Analysis of Multihop Wireless Transmissions

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Edis Mekić ◽  
Mihajlo Stefanović ◽  
Petar Spalević ◽  
Nikola Sekulović ◽  
Ana Stanković
Keyword(s):  
Performance Analysis ◽  
Communication Systems ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Wireless Communication Systems ◽  
Multihop Wireless ◽  
Ratio Of Random Variables ◽  
Probability Density Function Pdf

The distributions of random variables are of interest in many areas of science. In this paper, the probability density function (PDF) and cumulative distribution function (CDF) of ratio of products of two random variables and random variable are derived. Random variables are described with Rayleigh, Nakagami-m, Weibull, andα-μdistributions. An application of obtained results in performance analysis of multihop wireless communication systems in different transmission environments described in detail. The proposed mathematical analysis is also complemented by various graphically presented numerical results.

On Optimal Permutation Scheduling in Stochastic Proportionate Flowshops

1992 ◽  
Vol 6 (4) ◽  
pp. 513-523
Author(s):  
Michael Pinedo ◽  
Dequan Shaw ◽  
Xiuli Chao
Keyword(s):  
Likelihood Ratio ◽  
Stochastic Order ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Processing Times ◽  
Optimal Permutation ◽  
In Series ◽  
Holding Cost ◽  
Increasing Sequences

Consider m machines in series with unlimited intermediate buffers and n jobs available at time zero. The processing times of job j on all m machines are equal to a random variable Xj with distribution Fj. Various cost functions are analyzed using stochastic order relationships. First, we focus on minimizing where cj is the weight (holding cost) and Tj the completion time of job j. We establish that if are in a class of distributions we define as SIFR, and and are increasing sequences of likelihood ratio-ordered and stochastic-ordered random variables, respectively, the job sequence [1, 2, … n ] is optimal among all static permutation schedules. Second, for arbitrary processing time distributions, if is an increasing sequence of likelihood ratio-ordered (hazard rate-ordered) random variables and the costs are nonincreasing, then a general cost function is minimized by the job sequence [1,2,…, n] in the stochastic ordering (increasing convex ordering) sense.

scholarly journals Possibility of using CMS Maple to study laws of distribution of random variables

Radiotekhnika ◽  
2021 ◽  
pp. 128-134
Author(s):  
I. Moshchenko ◽  
O. Nikitenko ◽  
Yu.V. Kozlov
Keyword(s):  
Data Processing ◽  
Random Variables ◽  
Random Variable ◽  
Large Set ◽  
Practical Applications ◽  
Symbolic Calculations ◽  
Variable Distribution ◽  
Topic Distribution ◽  
Distribution Laws ◽  
Independent Work

The use of CMS Maple for students' practical and independent work is described. The study of random variable distribution laws is actual. Statistical calculations without computer are difficult and require many functional and quintiles tables of standard distributions. This does not contribute to feeling the element of novelty in the material being studied, to be able to arbitrarily change the conditions of tasks, etc., it takes a lot of time in solving applied production problems, which is inappropriate Thus to determine and research random variable distribution laws both in practical applications and in studying we must use special mathematical packages. The most extended of them are Mathcad, MatLab, Mathematica, Maple. Specialized statistical packages (SAS, SPSS, STATISTIKA, STATGRAPHICS) are not relevant to study. Their use for studying requires very high education level in mathematical statistics. Most of the existing math packages allow users to operate at random variables, including the Computer Mathematics System (CMS) Maple. Thus, the purpose of this article is a description of the studying possibilities of the random variables distribution laws with CMS Maple and the application of the acquired skills to the independent work of students. The Maple Statistics Library has a large set of commands for analyzing data, computing various numerical characteristics of random variables, graphing their distribution laws, and for statistical data processing. Thanks to a powerful set of statistical tools, the possibility of symbolic calculations and data processing of CMS Maple, wide possibilities of graphical interpretation of the results obtained not only in a static but also in a dynamic form, it is advisable to use it when studying the topic "Distribution Laws of Random Variables" in students' practical and independent work to use their acquired skills in solving applied problems of science and technology.

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

Sign in / Sign up

Export Citation Format

Share Document