A329285 Decimal expansion of the quantile z_0.9995 of the standard normal distribution.

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

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_0.9995.

This number can also be denoted as probit(0.9995), 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<=3.2905267314...) = 0.9995, P(X<=-3.2905267314...) = 0.0005.

Prog

(PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.0005)*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), this sequence (z_0.9995), A329286 (z_0.9999), A329287 (z_0.99999), A329363 (z_0.999999).

Sequence in context: A066045 A110866 A257958 * A211878 A340461 A060481

Adjacent sequences: A329282 A329283 A329284 * A329286 A329287 A329288

Keyword

nonn,cons

Author

Jianing Song, Nov 12 2019

Status

approved