The densities and distributions of the largest eigenvalue and the trace of a Beta–Wishart matrix

Author:

Drensky Vesselin1,Edelman Alan2,Genoar Tierney3,Kan Raymond4,Koev Plamen3ORCID

Affiliation:

1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria

2. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

3. Department of Mathematics, San Jose State University, 1 Washington Square, San Jose, CA 95192, USA

4. Joseph L. Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, Ontario, Canada M5S 3E6, Canada

Abstract

We present new expressions for the densities and distributions of the largest eigenvalue and the trace of a Beta–Wishart matrix. The series expansions for these expressions involve fewer terms than previously known results. For the trace, we also present a new algorithm that is linear in the size of the matrix and the degree of truncation, which is optimal.

Funder

National Science Foundation

San Jose State University

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics,Statistics, Probability and Uncertainty,Statistics and Probability,Algebra and Number Theory

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