Journal ArticleDOI
Discrete Approximations of Probability Distributions
Allen C. Miller,Thomas R Rice +1 more
TLDR
In this article, a new procedure based on gaussian quadrature is developed to decrease the error in the approximation to any desired level, which can be used to increase the accuracy.Abstract:
Practical limits on the size of most probabilistic models require that probability distributions be approximated by a few representative values and associated probabilities. This paper demonstrates that methods commonly used to determine discrete approximations of probability distributions systematically underestimate the moments of the original distribution. A new procedure based on gaussian quadrature is developed in this paper. It can be used to decrease the error in the approximation to any desired level.read more
Citations
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Journal ArticleDOI
An evidential reasoning approach for multiple-attribute decision making with uncertainty
Jian-Bo Yang,Madan G. Singh +1 more
TL;DR: A decision making procedure is proposed to rank alternatives in MADM problems with uncertainty to deal with uncertain decision knowledge in multiple-attribute decision making (MADM) problems with both quantitative and qualitative attributes.
Journal ArticleDOI
Generating Scenario Trees for Multistage Decision Problems
Kjetil Høyland,Stein W. Wallace +1 more
TL;DR: This paper presents a method based on nonlinear programming that can be used to generate a limited number of discrete outcomes that satisfy specified statistical properties, and argues that what are the relevant properties, will be problem dependent.
Journal ArticleDOI
Point Estimate Schemes to Solve the Probabilistic Power Flow
J.M. Morales,Juan Perez-Ruiz +1 more
TL;DR: In this article, four different Hong's point estimate schemes are presented and tested on the probabilistic power flow problem and compared against those obtained from the Monte Carlo simulation, showing that the use of the scheme provides the best performance when a high number of random variables, both continuous and discrete, are considered.
Journal ArticleDOI
An efficient point estimate method for probabilistic analysis
TL;DR: In this article, a new and efficient point estimate method is developed to calculate the statistical moments of a random quantity, Z, that is a function of n random variables, X. The method is an extension of Rosenblueth's two-point concentration method.
Journal ArticleDOI
Scenario tree generation for multiperiod financial optimization by optimal discretization
TL;DR: In this paper it is shown how a scenario tree may be constructed in an optimal manner on the basis of a simulation model of the underlying financial process by using a stochastic approximation technique.
References
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Book
Numerical Methods for Scientists and Engineers
TL;DR: This inexpensive paperback edition of a groundbreaking classic is unique in its emphasis on the frequency approach and its use in the solution of problems.