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A228438
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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.
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2
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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
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OFFSET
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-1,2
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COMMENTS
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The Pearson correlation coefficient where the maximum difference occurs is given by A228402.
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LINKS
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FORMULA
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2*sqrt((Pi-3)*(Pi+3))/Pi - 6/Pi*arcsin((2*sqrt((Pi-3)*(Pi+3))/Pi)/2).
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EXAMPLE
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0.018083177430872294003006565434951459128139228361067...
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MATHEMATICA
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c = Sqrt[4*Pi^2 - 36]/Pi; RealDigits[c - 6/Pi*ArcSin[c/2], 10, 110] (* T. D. Noe, Nov 04 2013 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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