A228438 Decimal expansion of the maximum difference between a Pearson correlation coefficient and a Spearman correlation coefficient, assuming a bivariate normal distribution and infinite sample size.

1, 8, 0, 8, 3, 1, 7, 7, 4, 3, 0, 8, 7, 2, 2, 9, 4, 0, 0, 3, 0, 0, 6, 5, 6, 5, 4, 3, 4, 9, 5, 1, 4, 5, 9, 1, 2, 8, 1, 3, 9, 2, 2, 8, 3, 6, 1, 0, 6, 7, 3, 0, 7, 4, 1, 5, 9, 8, 2, 3, 5, 3, 5, 5, 6, 3, 9, 7, 9, 4, 4, 8, 9, 9, 7, 0, 2, 2, 8, 6, 9, 8, 2, 1, 1, 1, 5, 6, 8, 7, 7, 7, 8, 3, 6, 8, 6, 1, 7, 8, 8, 1, 3, 0, 2

Offset

-1,2

Comments

The Pearson correlation coefficient where the maximum difference occurs is given by A228402.

Links

Iain Fox, Table of n, a(n) for n = -1..20000

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

2*sqrt((Pi-3)*(Pi+3))/Pi - 6/Pi*arcsin((2*sqrt((Pi-3)*(Pi+3))/Pi)/2).

Example

0.018083177430872294003006565434951459128139228361067...

Mathematica

c = Sqrt[4*Pi^2 - 36]/Pi; RealDigits[c - 6/Pi*ArcSin[c/2], 10, 110] (* T. D. Noe, Nov 04 2013 *)

Prog

(MATLAB) vpa('2*((pi-3)*(pi+3))^.5/pi-6/pi*asin( (2*((pi-3)*(pi+3))^.5/pi)/2)', 50)
(PARI) 2*sqrt((Pi-3)*(Pi+3))/Pi - 6/Pi*asin((2*sqrt((Pi-3)*(Pi+3))/Pi)/2) \\ Michel Marcus, Dec 17 2017
(PARI) { default(realprecision, 20080); x=100*(2*sqrt((Pi-3)*(Pi+3))/Pi - 6/Pi*asin((2*sqrt((Pi-3)*(Pi+3))/Pi)/2)); for (n=-1, 20000, d=floor(x); x=(x-d)*10; write("b228438.txt", n, " ", d)); } \ Iain Fox, Dec 17 2017

Crossrefs

Cf. A228402.

Sequence in context: A186981 A347159 A156744 * A021557 A242943 A358941

Adjacent sequences: A228435 A228436 A228437 * A228439 A228440 A228441

Keyword

nonn,cons

Author

Joost de Winter, Nov 02 2013

Status

approved