NDLI: On numerical calculation of probabilities according to Dirichlet distribution

Content Provider	Springer Nature Link
Author	Gouda, Ashraf A. Szántai, Tamás
Copyright Year	2009
Abstract	The main difficulty in numerical solution of probabilistic constrained stochastic programming problems is the calculation of the probability values according to the underlying multivariate probability distribution. In addition, when we are using a nonlinear programming algorithm for the solution of the problem, the calculation of the first and second order partial derivatives may also be necessary.In this paper we give solutions to the above problems in the case of Dirichlet distribution. For the calculation of the cumulative distribution function values, the Lauricella function series expansions will be applied up to 7 dimensions. For higher dimensions we propose the hypermultitree bound calculations and a variance reduction simulation procedure based on these bounds. There will be given formulae for the calculation of the first and second order partial derivatives, too. The common property of these formulae is that they involve only lower dimensional cumulative distribution function calculations. Numerical test results will also be presented.
Starting Page	185
Ending Page	200
Page Count	16
File Format	PDF
ISSN	02545330
Journal	Annals of Operations Research
Volume Number	177
Issue Number	1
e-ISSN	15729338
Language	English
Publisher	Springer US
Publisher Date	2009-08-25
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Dirichlet distribution Lauricella function Probability bounds Monte Carlo simulation Variance reduction Theory of Computation Combinatorics Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Management Science and Operations Research

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