On Necessary Conditions of Finite-Valued Random Variable Algebraic Approximation

2021 ◽  
Vol 42 (1) ◽  
pp. 217-221
Author(s):  
A. D. Yashunsky
Keyword(s):  
Necessary Conditions ◽  
Random Variable ◽  
Algebraic Approximation

scholarly journals Boundedness of one-dimensional branching Markov processes

1997 ◽  
Vol 10 (4) ◽  
pp. 307-332 ◽  
Author(s):  
F. I. Karpelevich ◽  
Yu. M. Suhov
Keyword(s):  
Markov Processes ◽  
Necessary Conditions ◽  
Random Variable ◽  
Expected Number ◽  
One Dimensional ◽  
Sufficient And Necessary Conditions ◽  
Type Boundary ◽  
The One ◽  
Branching Diffusions ◽  
Jump Markov Processes

A general model of a branching Markov process on ℝ is considered. Sufficient and necessary conditions are given for the random variable M=supt≥0max1≤k≤N(t)Ξk(t) to be finite. Here Ξk(t) is the position of the kth particle, and N(t) is the size of the population at time t. For some classes of processes (smooth branching diffusions with Feller-type boundary points), this results in a criterion stated in terms of the linear ODEσ2(x)2f″(x)+a(x)f′(x)=λ(x)(1−k(x))f(x). Here σ(x) and a(x) are the diffusion coefficient and the drift of the one-particle diffusion, respectively, and λ(x) and k(x) the intensity of branching and the expected number of offspring at point x, respectively. Similarly, for branching jump Markov processes the conditions are expressed in terms of the relations between the integral μ(x)∫π(x,dy)(f(y)−f(x)) and the product λ(x)(1−k(x))f(x), where λ(x) and k(x) are as before, μ(x) is the intensity of jumping at point x, and π(x,dy) is the distribution of the jump from x to y.

scholarly journals Capability measurement of non-standard parameters of manufacturing processes

2021 ◽  
Vol 1199 (1) ◽  
pp. 012089
Author(s):  
R Turisova ◽  
S Markulik
Keyword(s):  
Necessary Conditions ◽  
Classical Method ◽  
Random Variable ◽  
Customer Relationships ◽  
Manufacturing Processes ◽  
Manufacturing Companies ◽  
Method Of Calculation ◽  
Product Parameter ◽  
The Common ◽  
Quality Production

Abstract Capability measurement of manufacturing processes creates basic attributes for the production of conformity products, those that meet the necessary conditions in terms of tolerance limits for all important parameters. They are also important in the supplier-customer relationships context as one of the important easily predictable but highly effective indicators of the quality production of delivered products. In many manufacturing companies, the capability measurement is performed by using capability indicators, where the method of calculation is based on the assumption of normality of the distribution of the measured product parameter, as well as the assumption of constant median value but also variability during the monitored period. However, in practice we often are able to see such parameters of manufacturing products or processes, which do not meet the expectations required in the classical method of capability indexes calculation. The problems are usually in a different than normal models of the distribution of a random variable representing a specific parameter of a product or process, as well as in the excessive variability of median values during the time in these so-called non-standard parameters. There will be presented on the particular manufacturing product, how certain non-conformities occur during the capability indexes measurement indices in the classical way for selected non-standard parameters. The paper describes how it is possible to modify the common method of calculating the mentioned capability indexes in a simple way so that they are applicable in specific production conditions.

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

1998 ◽  
Vol 37 (03) ◽  
pp. 235-238 ◽  
Author(s):  
M. El-Taha ◽  
D. E. Clark
Keyword(s):  
Monte Carlo ◽  
Decision Trees ◽  
Computer Algebra ◽  
Taylor Series ◽  
Computer Algebra System ◽  
Random Variable ◽  
Monte Carlo Analysis ◽  
Normal Random Variable ◽  
Medical Decision ◽  
Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

OPTIMIZATION OF MARKOV SYSTEMS OF QUEUEING WITH WAITING TIME IN THE MATLAB SYSTEM

2017 ◽  
pp. 39-47
Author(s):  
Viktor Afonin ◽  
Vladimir Valer'evich Nikulin
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Random Variable ◽  
Model Systems ◽  
Queuing Systems ◽  
Input Flow ◽  
Continuous Random Variable ◽  
Input Stream ◽  
Time Intervals ◽  
Markov Systems

The article focuses on attempt to optimize two well-known Markov systems of queueing: a multichannel queueing system with finite storage, and a multichannel queueing system with limited queue time. In the Markov queuing systems, the intensity of the input stream of requests (requirements, calls, customers, demands) is subject to the Poisson law of the probability distribution of the number of applications in the stream; the intensity of service, as well as the intensity of leaving the application queue is subject to exponential distribution. In a Poisson flow, the time intervals between requirements are subject to the exponential law of a continuous random variable. In the context of Markov queueing systems, there have been obtained significant results, which are expressed in the form of analytical dependencies. These dependencies are used for setting up and numerical solution of the problem stated. The probability of failure in service is taken as a task function; it should be minimized and depends on the intensity of input flow of requests, on the intensity of service, and on the intensity of requests leaving the queue. This, in turn, allows to calculate the maximum relative throughput of a given queuing system. The mentioned algorithm was realized in MATLAB system. The results obtained in the form of descriptive algorithms can be used for testing queueing model systems during peak (unchanged) loads.

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