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A228402
Decimal expansion of the Pearson correlation coefficient where the difference between the Pearson correlation coefficient and the Spearman correlation coefficient is maximal, assuming a bivariate normal distribution and infinite sample size.
2
5, 9, 3, 6, 6, 4, 3, 7, 3, 9, 3, 1, 8, 0, 3, 5, 1, 4, 2, 9, 9, 8, 9, 0, 0, 6, 1, 9, 4, 5, 9, 7, 7, 3, 2, 4, 3, 6, 5, 4, 5, 5, 3, 6, 5, 2, 3, 9, 7, 3, 2, 7, 4, 1, 6, 8, 9, 2, 0, 2, 3, 2, 6, 2, 7, 2, 4, 8, 6, 4, 4, 2, 6, 9, 8, 3, 3, 7, 1, 1, 5, 1, 6, 6, 2, 1, 0, 1, 7, 7, 9, 8, 6, 8, 7, 5, 0, 8, 0, 1, 0, 9, 5, 8, 4, 6, 6
OFFSET
0,1
COMMENTS
The magnitude of the difference is provided in A228438.
LINKS
C. Croux and C. Dehon, Influence functions of the Spearman and Kendall correlation measures, Statistical Methods and Applications, 19(4), 497-515, 2010, (see Eq. 5).
R. Guérin, J. C. de Oliveira, and S. Weber, Adoption of bundled services with network externalities and correlated affinities, arXiv:1310.4429 [cs.NI], 2013.
FORMULA
Equals 2*sqrt((Pi-3)*(Pi+3))/Pi.
Equals sqrt(4*Pi^2 - 36)/Pi.
EXAMPLE
0.59366437393180351429989006194597732436545536523973...
MATHEMATICA
RealDigits[Sqrt[4*Pi^2 - 36]/Pi, 10, 110][[1]] (* T. D. Noe, Nov 04 2013 *)
PROG
(MATLAB) vpa('2*((pi-3)*(pi+3))^.5/pi', 50)
(PARI) sqrt(4*Pi^2-36)/Pi \\ G. C. Greubel, Apr 03 2017
CROSSREFS
Cf. A228438.
Sequence in context: A333155 A256500 A239545 * A154265 A198133 A111453
KEYWORD
nonn,cons
AUTHOR
Joost de Winter, Nov 02 2013
STATUS
approved