PMID: 11607637Mar 5, 1996Paper

Randomness and degrees of irregularity

Proceedings of the National Academy of Sciences of the United States of America
S M Pincus, B H Singer

Abstract

The fundamental question "Are sequential data random?" arises in myriad contexts, often with severe data length constraints. Furthermore, there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness--e.g., to evaluate the efficacy of therapy in medicine. We address both these issues from a computable framework via a quantification of regularity. ApEn (approximate entropy), defining maximal randomness for sequences of arbitrary length, indicating the applicability to sequences as short as N = 5 points. An infinite sequence formulation of randomness is introduced that retains the operational (and computable) features of the finite case. In the infinite sequence setting, we indicate how the "foundational" definition of independence in probability theory, and the definition of normality in number theory, reduce to limit theorems without rates of convergence, from which we utilize ApEn to address rates of convergence (of a deficit from maximal randomness), refining the aforementioned concepts in a computationally essential manner. Representative applications among many are indicated to assess (i) random number generation output; (ii) well-shuffled arrangements; and (iii) (the quality of) b...Continue Reading

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Citations

Feb 21, 2006·Experimental Brain Research·Justin KavanaghSteven Morrison
Aug 15, 2009·Experimental Brain Research·Janey Prodoehl, David E Vaillancourt
Apr 14, 2005·European Journal of Applied Physiology·J J KavanaghR S Barrett
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Jun 5, 2003·Chaos·J. A. GonzalezL. E. Guerrero
Jul 15, 2009·Proceedings of the National Academy of Sciences of the United States of America·P Van LeeuwenD H Grönemeyer
Nov 6, 2012·Proceedings of the National Academy of Sciences of the United States of America·Steve Pincus, Burton H Singer
Aug 3, 2010·The Journals of Gerontology. Series A, Biological Sciences and Medical Sciences·Ranganath MuniyappaMarc R Blackman
Aug 28, 1998·Current Opinion in Obstetrics & Gynecology·S M Pincus, M J Minkin
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Sep 11, 2004·Proceedings of the National Academy of Sciences of the United States of America·Steve Pincus, Rudolf E Kalman
Nov 26, 1996·Proceedings of the National Academy of Sciences of the United States of America·S M PincusJ D Veldhuis
Sep 2, 1998·Proceedings of the National Academy of Sciences of the United States of America·S Pincus, B H Singer
Apr 8, 2014·Proceedings of the National Academy of Sciences of the United States of America·Steve Pincus, Burton H Singer

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