A329284 Decimal expansion of the quantile z_0.999 of the standard normal distribution.

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

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_0.999.

This number can also be denoted as probit(0.999), 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<=3.0902323061...) = 0.999, P(X<=-3.0902323061...) = 0.001.

Prog

(PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.001)*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), this sequence (z_0.999), A329285 (z_0.9995), A329286 (z_0.9999), A329287 (z_0.99999), A329363 (z_0.999999).

Sequence in context: A259346 A239798 A019827 * A269557 A201581 A164597

Adjacent sequences: A329281 A329282 A329283 * A329285 A329286 A329287

Keyword

nonn,cons,changed

Author

Jianing Song, Nov 12 2019

Status

approved