A Note on the Expectation of an Irrational Function of a Random Variable

1968 ◽  
Vol 22 (3) ◽  
pp. 31
Author(s):  
C. S. Pillai
Keyword(s):  
Random Variable ◽  
Irrational Function

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.

Determination of Optimal Reserve between Two Machines in Series with the Repair Time has Change of Distribution after the Truncation Point

GIS Business ◽  
2019 ◽  
Vol 14 (6) ◽  
pp. 577-585
Author(s):  
T. Vivekanandan ◽  
S. Sachithanantham
Keyword(s):  
Real Life ◽  
Random Variable ◽  
Repair Time ◽  
Inventory Level ◽  
Optimal Size ◽  
Truncation Point ◽  
In Series ◽  
Optimal Reserve ◽  
Optimal Inventory Level ◽  
Two Machines

In inventory control, suitable models for various real life systems are constructed with the objective of determining the optimal inventory level.  A new type of inventory model using the so-called change of distribution property is analyzed in this paper. There are two machines M1 and M2  in series and the output of M1 is the input of M2. Hence a reserve inventory between M1 and M2 is to be maintained. The method of obtaining the optimal size of reserve inventory, assuming cost of excess inventory, cost of shortage and when the rate of consumption of M2  is a constant, has already been attempted.  In this paper, it is assumed that the repair time of M1  is a random variable and the distribution of the same undergoes a change of distribution  after the truncation point X0 , which is taken to be a random variable.  The optimal size of the reserve inventory is obtained under the above said  assumption . Numerical illustrations are also provided.

STRUCTURAL RELIABILITY ANALYSIS BASED ON P-BOXES

2020 ◽  
Vol 92 (6) ◽  
pp. 51-58
Author(s):  
S.A. SOLOVYEV ◽  
Keyword(s):  
Probability Distribution ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Epistemic Uncertainty ◽  
Random Variable ◽  
Strength Criterion ◽  
Structural Elements ◽  
Structural Element ◽  
Limit States ◽  
Distribution Shape

The article describes a method for reliability (probability of non-failure) analysis of structural elements based on p-boxes. An algorithm for constructing two p-blocks is shown. First p-box is used in the absence of information about the probability distribution shape of a random variable. Second p-box is used for a certain probability distribution function but with inaccurate (interval) function parameters. The algorithm for reliability analysis is presented on a numerical example of the reliability analysis for a flexural wooden beam by wood strength criterion. The result of the reliability analysis is an interval of the non-failure probability boundaries. Recommendations are given for narrowing the reliability boundaries which can reduce epistemic uncertainty. On the basis of the proposed approach, particular methods for reliability analysis for any structural elements can be developed. Design equations are given for a comprehensive assessment of the structural element reliability as a system taking into account all the criteria of limit states.

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