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Axioms 2015, 4(3), 268-274; doi:10.3390/axioms4030268

Closed-Form Representations of the Density Function and Integer Moments of the Sample Correlation Coefficient

Department of Statistical & Actuarial Sciences, The University of Western Ontario, London, ON N6A 5B7, Canada
Academic Editors: Angel Garrido and Hans J. Haubold
Received: 7 May 2015 / Revised: 8 June 2015 / Accepted: 18 June 2015 / Published: 20 July 2015
View Full-Text   |   Download PDF [217 KB, uploaded 20 July 2015]

Abstract

This paper provides a simplified representation of the exact density function of R, the sample correlation coefficient. The odd and even moments of R are also obtained in closed forms. Being expressed in terms of generalized hypergeometric functions, the resulting representations are readily computable. Some numerical examples corroborate the validity of the results derived herein. View Full-Text
Keywords: sample correlation coefficient; hypergeometric function; density function; moments sample correlation coefficient; hypergeometric function; density function; moments
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Provost, S.B. Closed-Form Representations of the Density Function and Integer Moments of the Sample Correlation Coefficient. Axioms 2015, 4, 268-274.

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