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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.
2
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
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
KEYWORD
nonn,cons
AUTHOR
Joost de Winter, Nov 02 2013
STATUS
approved