Peh Ng

Engin Sungur, Peh Ng, " A Decomposition of Copulas and Its Use." In Communications in Statistics--Theory and Methods: Regression Analysis, Volume ­­­­34, No. 12   pp. 2269-2282:   Taylor and Francis, Inc., 2005

ABSTRACT:   In this article, we create a decomposition that represents and describes the dependence structure between two variables. Since copulas provide a deep understanding of the dependence structure by eliminating the effects of the marginals, they play a key role in this study. We define a discretized copula density matrix and we decompose it into a set of permutation matrices by using the Birkhoff - von Neumann Theorem. This decomposition provides a way to effectively apply the concepts of copulas to solve problems in multivariate statistical data analysis.
 
KEY WORDS:  Birkhoff - von Neumann theorem, Copulas, Discretized copulas, Gini's measure, Permutation matrix, Doubly stochastic matrix, Prior probability.

 

Peh H. Ng, "Designing Efficient Snow Plow Routes: A Service-Learning Project," In Mathematics in Service to the Community: Concepts and Models for Service-Lerning in the Mathematical Sciences, MAA Notes #66, pp. 69-80, The Mathematical Association of America, 2005

ABSTRACT: We descibe our experience incorporating service-learning into a combinatorics and graph theory course. In particular, we present a discrete mathematical model which we used to design efficient snow plow routes for Morris, Minnesota. We also discuss several issues of service-learning within the course as well as beyond the classroom.