Year

2009

Paper Type

Master's Thesis

College

College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)

Department

Mathematics & Statistics

Committee Chairperson

Dr. Ping Sa

Second Advisor

Dr. Pali Sen

Rights Statement

http://rightsstatements.org/vocab/InC/1.0/

Third Advisor

Dr. James Gleaton

Abstract

Many distributions of multivariate data in the real world follow a non-normal model with distributions being skewed and/or heavy tailed. In studies in which multivariate non-normal distributions are needed, it is important for simulations of those variables to provide data that is close to the desired parameters while also being fast and easy to perform. Three algorithms for generating multivariate non-normal distributions are reviewed for accuracy, speed and simplicity. They are the Fleishman Power Method, the Fifth-Order Polynomial Transformation Method, and the Generalized Lambda Distribution Method. Simulations were run in order to compare the three methods by how well they generate bivariate distributions with the desired means, variances, skewness, kurtoses, and correlation, simplicity of the algorithms, and how quickly the desired distributions were calculated.

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