A092678 Decimal expansion of the probable error.

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

Offset: 0

Author

Eric W. Weisstein, Mar 03 2004

Keywords

• nonn
• cons

Comments

0.75 percentile of the normal probability distribution function. In a bilateral sense, normally distributed random values x are equally likely to fall inside the interval (-a*sigma, +a*sigma) as to fall outside, "a" being this constant. - Stanislav Sykora, Nov 08 2013

Examples

			InverseErf(1/2) * sqrt(2) = 0.674489750...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..9999
• Stanislav Sykora, PARI/GP scripts for NormalErrorFunctions.
• Eric Weisstein's World of Mathematics, Standard Normal Distribution
• Eric Weisstein's World of Mathematics, Probable Error

Crossrefs

Cf. A002193, A069286.

Programs

Mathematica

RealDigits[ Sqrt[2] InverseErf[1/2], 10, 111][[1]] (* Robert G. Wilson v, Feb 11 2015 *)

PARI

See the links.

PARI

solve(x=0,1,erfc(x)-1/2)*sqrt(2) \\ Charles R Greathouse IV, Oct 15 2015

Formula

Equals A069286 * A002193.