Title page for ETD etd-11012010-024209


Type of Document Dissertation
Author Shin, Kaeyoung
Author's Email Address pman93@vt.edu
URN etd-11012010-024209
Title Random Vector Generation on Large Discrete Spaces
Degree PhD
Department Industrial and Systems Engineering
Advisory Committee
Advisor Name Title
Pasupathy, Raghu Committee Chair
Nachlas, Joel A. Committee Member
Sarin, Subhash C. Committee Member
Taaffe, Michael R. Committee Member
Keywords
  • random vector generation
  • input modeling
  • stochastic simulation
Date of Defense 2010-10-15
Availability restricted
Abstract
This dissertation addresses three important open questions in the context of generating

random vectors having discrete support. The first question relates to the “NORmal To

Anything” (NORTA) procedure, which is easily the most widely used amongst methods for

general random vector generation. While NORTA enjoys such popularity, there remain issues

surrounding its efficient and correct implementation particularly when generating random

vectors having denumerable support. These complications stem primarily from having to

safely compute (on a digital computer) certain infinite summations that are inherent to

the NORTA procedure. This dissertation addresses the summation issue within NORTA

through the construction of easily computable truncation rules that can be applied for a

range of discrete random vector generation contexts.

The second question tackled in this dissertation relates to developing a customized algorithm

for generating multivariate Poisson random vectors. The algorithm developed (TREx)

is uniformly fast — about hundred to thousand times faster than NORTA — and presents

opportunities for straightforward extensions to the case of negative binomial marginal distributions.

The third and arguably most important question addressed in the dissertation is that

of exact nonparametric random vector generation on finite spaces. Specifically, it is wellknown

that NORTA does not guarantee exact generation in dimensions higher than two. This

represents an important gap in the random vector generation literature, especially in view of

contexts that stipulate strict adherence to the dependency structure of the requested random

vectors. This dissertation fully addresses this gap through the development of Maximum

Entropy methods. The methods are exact, very efficient, and work on any finite discrete

space with stipulated nonparametric marginal distributions. All code developed as part of

the dissertation was written in MATLAB, and is publicly accessible through the Web site

.

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