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.

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

G. C. Greubel, Table of n, a(n) for n = 0..10000

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

Adjacent sequences: A228399 A228400 A228401 * A228403 A228404 A228405

Keyword

nonn,cons

Author

Joost de Winter, Nov 02 2013

Status

approved