generating correlation matrices based on the boundaries of their coefficients基于边界生成关联矩阵的系数.pdfVIP

Generating Correlation Matrices Based on the Boundaries of Their Coefficients Kawee Numpacharoen1,2*, Amporn Atsawarungruangkit3 1 Financial Product Development, Kasikorn Securities, Bangkok, Thailand, 2 Department of Mathematics, Faculty of Science, Mahidol University, Bangkok, Thailand, 3 College of Medicine, Rangsit University, Bangkok, Thailand Abstract Correlation coefficients among multiple variables are commonly described in the form of matrices. Applications of such correlation matrices can be found in many fields, such as finance, engineering, statistics, and medicine. This article proposes an efficient way to sequentially obtain the theoretical bounds of correlation coefficients together with an algorithm to generate n |n correlation matrices using any bounded random variables. Interestingly, the correlation matrices generated by this method using uniform random variables as an example produce more extreme relationships among the variables than other methods, which might be useful for modeling complex biological systems where rare cases are very important. Citation: Numpacharoen K, Atsawarungruangkit A (2012) Generating Correlation Matrices Based on the Boundaries of Their Coefficients. PLoS ONE 7(11): e48902. doi:10.1371/journal.pone.0048902 ` Editor: Enrico Scalas, Universita del Piemonte Orientale, Italy Received August 27, 2012; Accepted October 1, 2012; Published November 12, 2012 Copyright: 2012 Numpacharoen, Atsawarungruangkit. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: The authors have no support or funding to report. Competing Interests: One of the authors (KN) is a paid emplo