A new method for building a discrete analogue to a continuous random variable based on minimization of a distance between distribution functions

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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Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽

10.3390/math9090981 ◽

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.

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Distributional Replication

Entropy ◽

10.3390/e23081063 ◽

2021 ◽

Vol 23 (8) ◽

pp. 1063

Author(s):

Brendan K. Beare

Keyword(s):

Hedge Fund ◽

Minimum Cost ◽

Random Variable ◽

Optimal Approximation ◽

Regularity Conditions ◽

Return Distribution ◽

Continuous Random Variable ◽

Hedge Fund Replication ◽

Market Index ◽

Fund Return

A function which transforms a continuous random variable such that it has a specified distribution is called a replicating function. We suppose that functions may be assigned a price, and study an optimization problem in which the cheapest approximation to a replicating function is sought. Under suitable regularity conditions, including a bound on the entropy of the set of candidate approximations, we show that the optimal approximation comes close to achieving distributional replication, and close to achieving the minimum cost among replicating functions. We discuss the relevance of our results to the financial literature on hedge fund replication; in this case, the optimal approximation corresponds to the cheapest portfolio of market index options which delivers the hedge fund return distribution.

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Transformation of circular random variables based on circular distribution functions

Filomat ◽

10.2298/fil1817931m ◽

2018 ◽

Vol 32 (17) ◽

pp. 5931-5947

Author(s):

Hatami Mojtaba ◽

Alamatsaz Hossein

Keyword(s):

Distribution Function ◽

Random Variables ◽

Real Data ◽

Random Variable ◽

Distribution Functions ◽

Likelihood Method ◽

Circular Distribution ◽

Data Set ◽

Trigonometric Moments ◽

Von Mises

In this paper, we propose a new transformation of circular random variables based on circular distribution functions, which we shall call inverse distribution function (id f ) transformation. We show that M?bius transformation is a special case of our id f transformation. Very general results are provided for the properties of the proposed family of id f transformations, including their trigonometric moments, maximum entropy, random variate generation, finite mixture and modality properties. In particular, we shall focus our attention on a subfamily of the general family when id f transformation is based on the cardioid circular distribution function. Modality and shape properties are investigated for this subfamily. In addition, we obtain further statistical properties for the resulting distribution by applying the id f transformation to a random variable following a von Mises distribution. In fact, we shall introduce the Cardioid-von Mises (CvM) distribution and estimate its parameters by the maximum likelihood method. Finally, an application of CvM family and its inferential methods are illustrated using a real data set containing times of gun crimes in Pittsburgh, Pennsylvania.

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A Single Valued Neutrosophic Inventory Model with Neutrosophic Random Variable

10.54216/ijns.010201 ◽

2020 ◽

pp. 52-63

Author(s):

M. Mullai*, K. Sangeetha, R. Surya, G. Madhan kumar, R. Jeyabalan ◽

◽

S. Broumi

Keyword(s):

Random Variables ◽

Random Variable ◽

Inventory Model ◽

Newsvendor Problem ◽

New Method ◽

Optimal Sequence ◽

Average Value ◽

Proposed Model

This paper presents the problematic period of neutrosophic inventory in an inaccurate and unsafe mixed environment. The purpose of this paper is to present demand as a neutrosophic random variable. For this model, a new method is developed for determining the optimal sequence size in the presence of neutrosophic random variables. Where to get optimality by gradually expressing the average value of integration. The newsvendor problem is used to describe the proposed model.

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Method for Constructing a Confidence Interval for the Variance of a Random Variable

Vestnik NSUEM ◽

10.34020/2073-6495-2021-3-146-155 ◽

2021 ◽

pp. 146-155

Author(s):

A. V. Ganicheva ◽

A. V. Ganichev

Keyword(s):

Probability Distribution ◽

Confidence Interval ◽

Random Variable ◽

New Method ◽

Interval Estimate ◽

Normal Law

The problem of reducing the number of observations for constructing a confidence interval of variance with a given degree of accuracy and reliability is considered. The new method of constructing an interval estimate of variance developed in the article is formulated by three statements and justified by four proven theorems. Formulas for calculating the required number of observations depending on the accuracy and reliability of the estimate are derived. The results of the calculations are presented in the table and shown in the diagram. The universality and effectiveness of this method is shown. The universality of the method lies in the fact that it is applicable to any laws of probability distribution, and not only for the normal law. The effectiveness of the developed method is justified by comparing its performance with other known methods.

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Two-player zero-sum stochastic differential games with random horizon

Advances in Applied Probability ◽

10.1017/apr.2019.47 ◽

2019 ◽

Vol 51 (4) ◽

pp. 1209-1235

Author(s):

M. Ferreira ◽

D. Pinheiro ◽

S. Pinheiro

Keyword(s):

Viscosity Solution ◽

Nonlinear Partial Differential Equation ◽

Random Variable ◽

Planning Horizon ◽

Continuous Random Variable ◽

State Variable ◽

Random Horizon ◽

Hamilton Jacobi Bellman ◽

Zero Sum ◽

Random Planning Horizon

AbstractWe consider a two-player zero-sum stochastic differential game with a random planning horizon and diffusive state variable dynamics. The random planning horizon is a function of a non-negative continuous random variable, which is assumed to be independent of the Brownian motion driving the state variable dynamics. We study this game using a combination of dynamic programming and viscosity solution techniques. Under some mild assumptions, we prove that the value of the game exists and is the unique viscosity solution of a certain nonlinear partial differential equation of Hamilton–Jacobi–Bellman–Isaacs type.

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Study of the Drell-Yan process with the pair-production of polarized tau leptons in collisions of polarized proton beams

EPJ Web of Conferences ◽

10.1051/epjconf/201922203021 ◽

2019 ◽

Vol 222 ◽

pp. 03021

Author(s):

A. Aleshko ◽

E. Boos ◽

V. Bunichev

Keyword(s):

Parton Distribution ◽

Polarization State ◽

Distribution Functions ◽

Hadronic Decay ◽

New Method ◽

Tau Leptons ◽

Parton Distribution Functions ◽

Accuracy Of Measurements ◽

Polarized Proton

The new method for studying polarized parton distribution functions via the Drell-Yan process with tau production is proposed. The hadronic decay of tau to single charged pi-meson and neutrino is utilised for determination of the polarization state of the tau-lepton. The key feature of our approach is that we do not sum over the polarizations states of tau, but preserve this information through energies ofpions produced in corresponding decays. The new method in addition to existing ones should improve the accuracy of measurements of polarized structure functions of hadrons. In the current work, the feasibility of such an approach is assessed through numerical simulations.

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A Note on Nonparametric Estimation of the CTE

Astin Bulletin ◽

10.2143/ast.39.2.2044655 ◽

2009 ◽

Vol 39 (2) ◽

pp. 717-734 ◽

Cited By ~ 7

Author(s):

Bangwon Ko ◽

Ralph P. Russo ◽

Nariankadu D. Shyamalkumar

Keyword(s):

Order Term ◽

Random Variable ◽

Small Samples ◽

Closed Form Expression ◽

Form Expression ◽

Continuous Random Variable ◽

Underlying Distribution ◽

First Order ◽

Bootstrap Approach ◽

Conditional Tail Expectation

AbstractThe α-level Conditional Tail Expectation (CTE) of a continuous random variable X is defined as its conditional expectation given the event {X > qα} where qα represents its α-level quantile. It is well known that the empirical CTE (the average of the n (1 – α) largest order statistics in a sample of size n) is a negatively biased estimator of the CTE. This bias vanishes as the sample size increases, but in small samples can be significant. In this article it is shown that an unbiased nonparametric estimator of the CTE does not exist. In addition, the asymptotic behavior of the bias of the empirical CTE is studied, and a closed form expression for its first order term is derived. This expression facilitates the study of the behavior of the empirical CTE with respect to the underlying distribution, and suggests an alternative (to the bootstrap) approach to bias correction. The performance of the resulting estimator is assessed via simulation.

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