scholarly journals A Single Valued Neutrosophic Inventory Model with Neutrosophic Random Variable

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.

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.

scholarly journals Fully degenerate Bell polynomials associated with degenerate Poisson random variables

2021 ◽  
Vol 19 (1) ◽  
pp. 284-296
Author(s):  
Hye Kyung Kim
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Combinatorial Identities ◽  
Bell Polynomials ◽  
Poisson Random Variable ◽  
Central Moments ◽  
Special Polynomials ◽  
Special Numbers And Polynomials ◽  
New Type ◽  
Two Parameters

Abstract Many mathematicians have studied degenerate versions of quite a few special polynomials and numbers since Carlitz’s work (Utilitas Math. 15 (1979), 51–88). Recently, Kim et al. studied the degenerate gamma random variables, discrete degenerate random variables and two-variable degenerate Bell polynomials associated with Poisson degenerate central moments, etc. This paper is divided into two parts. In the first part, we introduce a new type of degenerate Bell polynomials associated with degenerate Poisson random variables with parameter α > 0 \alpha \hspace{-0.15em}\gt \hspace{-0.15em}0 , called the fully degenerate Bell polynomials. We derive some combinatorial identities for the fully degenerate Bell polynomials related to the n n th moment of the degenerate Poisson random variable, special numbers and polynomials. In the second part, we consider the fully degenerate Bell polynomials associated with degenerate Poisson random variables with two parameters α > 0 \alpha \gt 0 and β > 0 \beta \hspace{-0.15em}\gt \hspace{-0.15em}0 , called the two-variable fully degenerate Bell polynomials. We show their connection with the degenerate Poisson central moments, special numbers and polynomials.

A Note on the Accuracy of Normal Approximation of Random Quantities

2021 ◽  
Vol 73 (1) ◽  
pp. 62-67
Author(s):  
Ibrahim A. Ahmad ◽  
A. R. Mugdadi
Keyword(s):  
Sample Size ◽  
Order Statistic ◽  
Normal Approximation ◽  
Order Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Limiting Distribution ◽  
Exact Order ◽  
Fixed Sample ◽  
Independent Identically Distributed

For a sequence of independent, identically distributed random variable (iid rv's) [Formula: see text] and a sequence of integer-valued random variables [Formula: see text], define the random quantiles as [Formula: see text], where [Formula: see text] denote the largest integer less than or equal to [Formula: see text], and [Formula: see text] the [Formula: see text]th order statistic in a sample [Formula: see text] and [Formula: see text]. In this note, the limiting distribution and its exact order approximation are obtained for [Formula: see text]. The limiting distribution result we obtain extends the work of several including Wretman[Formula: see text]. The exact order of normal approximation generalizes the fixed sample size results of Reiss[Formula: see text]. AMS 2000 subject classification: 60F12; 60F05; 62G30.

scholarly journals Novel Route Planning Method to Improve the Operational Efficiency of Capacitated Operations. Case: Application of Organic Fertilizer

2021 ◽  
Vol 3 (3) ◽  
pp. 458-477
Author(s):  
Mahdi Vahdanjoo ◽  
Claus G. Sorensen
Keyword(s):  
Organic Fertilizer ◽  
Route Planning ◽  
Fertilizer Application ◽  
Operational Efficiency ◽  
Application Rate ◽  
Simultaneous Optimization ◽  
Limiting Factor ◽  
Application Process ◽  
Optimal Sequence ◽  
Proposed Model

A field area coverage-planning algorithm has been developed for the optimization and simulation of capacitated field operations such as the organic fertilizer application process. The proposed model provides an optimal coverage plan, which includes the optimal sequence of the visited tracks with a designated application rate. The objective of this paper is to present a novel approach for route planning involving two simultaneous optimization criteria, non-working distance minimization and the optimization of application rates, for the capacitated field operations such as organic fertilizer application to improve the overall operational efficiency. The study and the developed algorithm have shown that it is possible to generate the optimized coverage plan based on the required defined capacity of the distributer. In this case, the capacity of the distributer is not considered a limiting factor for the farmers. To validate this new method, a shallow injection application process was considered, and the results of applying the optimization algorithm were compared with the conventional methods. The results show that the proposed method increase operational efficiency by 19.7%. Furthermore, the applicability of the proposed model in robotic application were demonstrated by way of two defined scenarios.

scholarly journals On Newcomb's method of investigating periodicities and its application to Brückner's weather cycle

1914 ◽  
Vol 90 (619) ◽  
pp. 349-355
Keyword(s):  
Thermal Radiation ◽  
The Other ◽  
New Method ◽  
Critical Examination ◽  
Numerical Work ◽  
Average Value ◽  
Other Hand ◽  
Relationship Of ◽  
The Relationship ◽  
Great Simplicity

During the last few years of his life Prof. Simon Newcomb was keenly interested in the problem of periodicities, and devised a new method for their investigation. This method is explained, and to some extent applied, in a paper entitled "A Search for Fluctuations in the Sun's Thermal Radiation through their Influence on Terrestrial Temperature." The importance of the question justifies a critical examination of the relationship of the older methods to that of Newcomb, and though I do not agree with his contention that his process gives us more than can be obtained from Fourier's analysis, it has the advantage of great simplicity in its numerical work, and should prove useful in a certain, though I am afraid, very limited field. Let f ( t ) represent a function of a variable which we may take to be the time, and let the average value of the function be zero. Newcomb examines the sum of the series f ( t 1 ) f ( t 1 + τ) + f ( t 2 ) f ( t 2 + τ) + f ( t 3 ) f ( t 3 + τ) + ..., where t 1 , t 2 , etc., are definite values of the variable which are taken to lie at equal distances from each other. If the function be periodic so as to repeat itself after an interval τ, the products are all squares and each term is positive. If, on the other hand, the periodic time be 2τ, each product will be negative and the sum itself therefore negative. It is easy to see that if τ be varied continuously the sum of the series passes through maxima and minima, and the maxima will indicated the periodic time, or any of its multiples.

INFORMATION AND UNCERTAINTY IN A QUEUING SYSTEM

2007 ◽  
Vol 21 (3) ◽  
pp. 361-380 ◽  
Author(s):  
Refael Hassin
Keyword(s):  
Service Quality ◽  
Random Variables ◽  
Random Variable ◽  
Queuing System ◽  
Service Rate ◽  
Single Server ◽  
Profit Function

This article deals with the effect of information and uncertainty on profits in an unobservable single-server queuing system. We consider scenarios in which the service rate, the service quality, or the waiting conditions are random variables that are known to the server but not to the customers. We ask whether the server is motivated to reveal these parameters. We investigate the structure of the profit function and its sensitivity to the variance of the random variable. We consider and compare variations of the model according to whether the server can modify the service price after observing the realization of the random variable.

The central limit problem for trimmed sums

1987 ◽  
Vol 102 (2) ◽  
pp. 329-349 ◽  
Author(s):  
Philip S. Griffin ◽  
William E. Pruitt
Keyword(s):  
Distribution Function ◽  
Random Variables ◽  
Random Variable ◽  
Limit Problem ◽  
Absolute Value ◽  
Trimmed Sums ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Central Limit Problem ◽  
Trimmed Sum

Let X, X1, X2,… be a sequence of non-degenerate i.i.d. random variables with common distribution function F. For 1 ≤ j ≤ n, let mn(j) be the number of Xi satisfying either |Xi| > |Xj|, 1 ≤ i ≤ n, or |Xi| = |Xj|, 1 ≤ i ≤ j, and let (r)Xn = Xj if mn(j) = r. Thus (r)Xn is the rth largest random variable in absolute value from amongst X1, …, Xn with ties being broken according to the order in which the random variables occur. Set (r)Sn = (r+1)Xn + … + (n)Xn and write Sn for (0)Sn. We will refer to (r)Sn as a trimmed sum.

Poisson approximation for a sum of dependent indicators: an alternative approach

2002 ◽  
Vol 34 (03) ◽  
pp. 609-625 ◽  
Author(s):  
N. Papadatos ◽  
V. Papathanasiou
Keyword(s):  
Total Variation ◽  
Upper Bound ◽  
Random Variables ◽  
Random Variable ◽  
Poisson Approximation ◽  
Total Variation Distance ◽  
Poisson Random Variable ◽  
Birthday Problem ◽  
Alternative Approach ◽  
Variation Distance

The random variablesX1,X2, …,Xnare said to be totally negatively dependent (TND) if and only if the random variablesXiand ∑j≠iXjare negatively quadrant dependent for alli. Our main result provides, for TND 0-1 indicatorsX1,x2, …,Xnwith P[Xi= 1] =pi= 1 - P[Xi= 0], an upper bound for the total variation distance between ∑ni=1Xiand a Poisson random variable with mean λ ≥ ∑ni=1pi. An application to a generalized birthday problem is considered and, moreover, some related results concerning the existence of monotone couplings are discussed.

scholarly journals On Exact Sampling of Nonnegative Infinitely Divisible Random Variables

2012 ◽  
Vol 44 (3) ◽  
pp. 842-873 ◽  
Author(s):  
Zhiyi Chi
Keyword(s):  
Basic Result ◽  
Random Variables ◽  
Random Variable ◽  
Fixed Number ◽  
Rejection Sampling ◽  
Infinitely Divisible ◽  
Exact Sampling ◽  
Special Cases ◽  
Wide Range ◽  
Lévy Density

Nonnegative infinitely divisible (i.d.) random variables form an important class of random variables. However, when this type of random variable is specified via Lévy densities that have infinite integrals on (0, ∞), except for some special cases, exact sampling is unknown. We present a method that can sample a rather wide range of such i.d. random variables. A basic result is that, for any nonnegative i.d. random variable X with its Lévy density explicitly specified, if its distribution conditional on X ≤ r can be sampled exactly, where r > 0 is any fixed number, then X can be sampled exactly using rejection sampling, without knowing the explicit expression of the density of X. We show that variations of the result can be used to sample various nonnegative i.d. random variables.

scholarly journals Improving the Asmussen–Kroese-Type Simulation Estimators

2012 ◽  
Vol 49 (4) ◽  
pp. 1188-1193 ◽  
Author(s):  
Samim Ghamami ◽  
Sheldon M. Ross
Keyword(s):  
Monte Carlo ◽  
Nonnegative Integer ◽  
Rare Event ◽  
Random Variables ◽  
Random Variable ◽  
Heavy Tailed ◽  
Independent Identically Distributed

The Asmussen–Kroese Monte Carlo estimators of P(Sn > u) and P(SN > u) are known to work well in rare event settings, where SN is the sum of independent, identically distributed heavy-tailed random variables X1,…,XN and N is a nonnegative, integer-valued random variable independent of the Xi. In this paper we show how to improve the Asmussen–Kroese estimators of both probabilities when the Xi are nonnegative. We also apply our ideas to estimate the quantity E[(SN-u)+].

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