Means and variances of stochastic vector products with applications to random linear models
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Authors
Brown, Gerald G.
Rutemiller, Herbert C.
Subjects
Random Linear Models
Stochastic Programming
Chance Constrained Linear Programming
Tchebycheff Inequalities
Joint Tchebycheff Bounds
Dependent Stochastic Vector Products
Moments of Dependent Stochastic Vector Products
Stochastic Programming
Chance Constrained Linear Programming
Tchebycheff Inequalities
Joint Tchebycheff Bounds
Dependent Stochastic Vector Products
Moments of Dependent Stochastic Vector Products
Advisors
Date of Issue
1977-02
Date
1977-02
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
Many mathematical models in operations research require computation of products of vectors whose elements are random variables. Unfortunately, analytic results for functions of interest are only obtained through highly restrictive, often unrealistic, choices of prior densities for the vectors' elements. Often, an investigation is performed by discretizing the random variables at point-quantile levels, or by outright simulation. This paper addresses the problem of characterizing the inner product of two stochastic vectors with arbitrary multivariate densities. Expressions for means of variances of vector products are obtained, and used to make Tchebycheff-type probability statements. Included are applications to stochastic programming models. (Author)
Type
Technical Report
Description
Series/Report No
Department
Identifiers
NPS Report Number
NPS55-77-6
Sponsors
Naval Postgraduate School
Monterey, California
Funder
Format
Citation
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.