A329287 Decimal expansion of the quantile z_0.99999 of the standard normal distribution.

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

Offset

1,1

Comments

z_p is the number z such that Phi(z) = p, where Phi(x) = Integral_{t=-oo..x} (1/sqrt(2*Pi))*exp(-t^2/2)*dt is the cumulative distribution function of the standard normal distribution. This sequence gives z_0.99999.

This number can also be denoted as probit(0.99999), where probit(p) is the inverse function of Phi(x). See the Wikipedia link below.

Links

Table of n, a(n) for n=1..91.

Eric Weisstein's World of Mathematics, Quantile Function.

Wikipedia, Probit.

Example

If X ~ N(0,1), then P(X<=4.2648907939...) = 0.99999, P(X<=-4.2648907939...) = 0.00001.

Mathematica

RealDigits[(x /. FindRoot[50000*Erfc[x] == 1, {x, 1, 2}, WorkingPrecision -> 120]) * Sqrt[2]][[1]] (* Amiram Eldar, Apr 16 2026 *)

Prog

(PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.00001)*sqrt(2)

Crossrefs

Quantiles of the standard normal distribution: A092678 (z_0.75), A329280 (z_0.9), A329281 (z_0.95), A329282 (z_0.99), A329283 (z_0.995), A329284 (z_0.999), A329285 (z_0.9995), A329286 (z_0.9999), this sequence (z_0.99999), A329363 (z_0.999999).

Sequence in context: A253629 A327095 A176836 * A368665 A372529 A021705

Adjacent sequences: A329284 A329285 A329286 * A329288 A329289 A329290

Keyword

nonn,cons

Author

Jianing Song, Nov 12 2019

Status

approved