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.

PERCEPTION-BASED ESTIMATIONS OF FUZZY RANDOM VARIABLES: LINEARITY AND CONVEXITY

2008 ◽  
Vol 16 (supp01) ◽  
pp. 71-87 ◽  
Author(s):  
YUJI YOSHIDA
Keyword(s):  
Random Variables ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Fuzzy Random Variables ◽  
Engineering Economics ◽  
Random Events ◽  
Fuzzy Random

A set of perceived random events is given by a fuzzy random variable, and an estimation of real random variables is represented by a functional on real random variables. The perception-based extension of estimation regarding random events is introduced, extending the functional to a functional of fuzzy random variables. This paper discusses some conditions and various properties of the extended estimations, for example, monotonicity, continuity, linearity, sub-additivity/super-additivity, convexity/concavity. Several examples of the perception-based extended estimations are investigated. This paper analyzes the general cases, where the estimations do not have monotone properties, from the viewpoint of convexity/concavity. The results can be applicable to other estimations in engineering, economics and so on.

DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

2001 ◽  
Vol 09 (01) ◽  
pp. 39-53 ◽  
Author(s):  
RONALD R. YAGER
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Cumulative Distribution ◽  
General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

Estimating the cumulative distribution function for the linear combination of gamma random variables

2017 ◽  
Vol 20 (5) ◽  
pp. 939-951
Author(s):  
Amal Almarwani ◽  
Bashair Aljohani ◽  
Rasha Almutairi ◽  
Nada Albalawi ◽  
Alya O. Al Mutairi
Keyword(s):  
Distribution Function ◽  
Linear Combination ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Cumulative Distribution

scholarly journals Generalized Variability Orderings among Nonnegative Fuzzy Random Variables

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
S. Ramasubramanian ◽  
P. Mahendran
Keyword(s):  
Distribution Function ◽  
Integral Inequality ◽  
Random Variables ◽  
Fuzzy Random Variables ◽  
Equivalent Conditions ◽  
New Better Than Used ◽  
Better Than ◽  
Fuzzy Random

The variability ordering for more and less variables of fuzzy random variables in terms of its distribution function is defined. A property of new better than used in expectation (NBUE) and new worse than used in expectation (NWUE) is derived as an application to the variability ordering of fuzzy random variables. The concept of generalized variability orderings of nonnegative fuzzy random variables representing lifetime of components is introduced. The<Pdomination is a generalized variability ordering. We proposed an integral inequality to the case of fuzzy random variables using<Pordering. The results included equivalent conditions which justify the generalized variability orderings.

scholarly journals Nondecreasing Lower Bound on the Poisson Cumulative Distribution Function for z Standard Deviations Above the Mean

2013 ◽  
Vol 50 (4) ◽  
pp. 909-917
Author(s):  
M. Bondareva
Keyword(s):  
Distribution Function ◽  
Lower Bound ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Step Function ◽  
Cumulative Distribution ◽  
Control Parameters ◽  
Poisson Random Variable ◽  
The Mean ◽  
Standard Deviations

In this paper we discuss a nondecreasing lower bound for the Poisson cumulative distribution function (CDF) at z standard deviations above the mean λ, where z and λ are parameters. This is important because the normal distribution as an approximation for the Poisson CDF may overestimate or underestimate its value. A sharp nondecreasing lower bound in the form of a step function is constructed. As a corollary of the bound's properties, for a given percent α and parameter λ, the minimal z is obtained such that, for any Poisson random variable with the mean greater or equal to λ, its αth percentile is at most z standard deviations above its mean. For Poisson distributed control parameters, the corollary allows simple policies measuring performance in terms of standard deviations from a benchmark.

Gaussian Quadrature GQ Used to Accurately Approximate the Relative Weights of Reserves, Contingent Resources, and Prospective Resources Through A Cumulative Distribution Function

2021 ◽  
Author(s):  
Nefeli Moridis ◽  
W. John Lee ◽  
Wayne Sim ◽  
Thomas Blasingame
Keyword(s):  
Distribution Function ◽  
Standard Deviation ◽  
Cumulative Distribution Function ◽  
Gaussian Quadrature ◽  
Random Variables ◽  
Cumulative Distribution ◽  
Production Data ◽  
Discrete Random Variables ◽  
Percent Difference ◽  
The Relationship

Abstract The objective of this work is to numerically estimate the fraction of Reserves assigned to each Reserves category of the PRMS matrix through a cumulative distribution function. We selected 38 wells from a Permian Basin dataset available to Texas A&M University. Previous work has shown that Swanson's Mean, which relates the Reserves categories through a cdf of a normal distribution, is an inaccurate method to determine the relationship of the Reserves categories with asymmetric distributions. Production data are lognormally distributed, regardless of basin type, thus cannot follow the SM concept. The Gaussian Quadrature (GQ) provides a methodology to accurately estimate the fraction of Reserves that lie in 1P, 2P, and 3P categories – known as the weights. Gaussian Quadrature is a numerical integration method that uses discrete random variables and a distribution that matches the original data. For this work, we associate the lognormal cumulative distribution function (CDF) with a set of discrete random variables that replace the production data, and determine the associated probabilities. The production data for both conventional and unconventional fields are lognormally distributed, thus we expect that this methodology can be implemented in any field. To do this, we performed probabilistic decline curve analysis (DCA) using Arps’ Hyperbolic model and Monte Carlo simulation to obtain the 1P, 2P, and 3P volumes, and calculated the relative weights of each Reserves category. We performed probabilistic rate transient analysis (RTA) using a commercial software to obtain the 1P, 2P, and 3P volumes, and calculated the relative weights of each Reserves category. We implemented the 3-, 5-, and 10-point GQ to obtain the weight and percentiles for each well. Once this was completed, we validated the GQ results by calculating the percent-difference between the probabilistic DCA, RTA, and GQ results. We increase the standard deviation to account for the uncertainty of Contingent and Prospective resources and implemented 3-, 5-, and 10-point GQ to obtain the weight and percentiles for each well. This allows us to also approximate the weights of these volumes to track them through the life of a given project. The probabilistic DCA, RTA and Reserves results indicate that the SM is an inaccurate method for estimating the relative weights of each Reserves category. The 1C, 2C, 3C, and 1U, 2U, and 3U Contingent and Prospective Resources, respectively, are distributed in a similar way but with greater variance, incorporated in the standard deviation. The results show that the GQ is able to capture an accurate representation of the Reserves weights through a lognormal CDF. Based on the proposed results, we believe that the GQ is accurate and can be used to approximate the relationship between the PRMS categories. This relationship will aid in booking Reserves to the SEC because it can be recreated for any field. These distributions of Reserves and resources other than Reserves (ROTR) are important for planning and for resource inventorying. The GQ provides a measure of confidence on the prediction of the Reserves weights because of the low percent difference between the probabilistic DCA, RTA, and GQ weights. This methodology can be implemented in both conventional and unconventional fields.

Study on Collaborative R&D Strategy between Manufacturer and Supplier Based on Uncertain Demand and Exchange Rate

2014 ◽  
Vol 1006-1007 ◽  
pp. 566-571
Author(s):  
Rui Wang ◽  
Xi Feng Li ◽  
Shuang Zhao ◽  
Jiang Yun Wang
Keyword(s):  
Exchange Rate ◽  
Development Strategy ◽  
Supply And Demand ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Market Demand ◽  
Fuzzy Random Variables ◽  
Hybrid Intelligent Algorithms ◽  
Better Than ◽  
Fuzzy Random

Imbalance of supply and demand relation in international market and the increasing volatility of exchange rate force the manufacturer to make reasonable R&D (Research and Development) strategy under turbulent market environment, which has become particularly important to enhance the international competitiveness. This paper presents a fuzzy random variable with multifold uncertain attribute to depict the increasing fluctuation of the market demand and the exchange rate, and thus construct two bilevel programming models with fuzzy random variables, which aims to compare two different R&D strategies: manufacturer involved in R&D independently and joint R&D of manufacturer and supplier. According to the characteristics of the two models, this paper designs the corresponding hybrid intelligent algorithms. The results of the two models in numerical examples show that: collaborative R&D strategy between manufacturer and supplier is better than manufacturer’s independent R&D strategy and the optimal proportion of R&D in this paper can be obtained: the supplier shares 50% of the total R&D cost.

ON CUMULATIVE RESIDUAL EXTROPY

2019 ◽  
Vol 34 (4) ◽  
pp. 605-625 ◽  
Author(s):  
S. M. A. Jahanshahi ◽  
H. Zarei ◽  
A. H. Khammar
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Alternative Measure ◽  
Numerical Examples ◽  
Cumulative Residual ◽  
Measure Of Uncertainty

Recently, an alternative measure of uncertainty called extropy is proposed by Lad et al. [12]. The extropy is a dual of entropy which has been considered by researchers. In this article, we introduce an alternative measure of uncertainty of random variable which we call it cumulative residual extropy. This measure is based on the cumulative distribution function F. Some properties of the proposed measure, such as its estimation and applications, are studied. Finally, some numerical examples for illustrating the theory are included.

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