A329282 Decimal expansion of the quantile z_0.99 of the standard normal distribution.

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

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_0.99 (also called the 99th percentile).

This number can also be denoted as probit(0.99), 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<=2.3263478740...) = 0.99, P(X<=-2.3263478740...) = 0.01.

Prog

(PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.01)*sqrt(2)

Crossrefs

Quantiles of the standard normal distribution: A092678 (z_0.75), A329280 (z_0.9), A329281 (z_0.95), this sequence (z_0.99), A329283 (z_0.995), A329284 (z_0.999), A329285 (z_0.9995), A329286 (z_0.9999), A329287 (z_0.99999), A329363 (z_0.999999).

Sequence in context: A316608 A033031 A134060 * A197289 A161888 A347859

Adjacent sequences: A329279 A329280 A329281 * A329283 A329284 A329285

Keyword

nonn,cons

Author

Jianing Song, Nov 12 2019

Status

approved