A329283 Decimal expansion of the quantile z_0.995 of the standard normal distribution.

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

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_0.995.

This number can also be denoted as probit(0.995), 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<=2.5758293035...) = 0.995, P(X<=-2.5758293035...) = 0.005.

Prog

(PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.005)*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), this sequence (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: A011038 A079378 A066035 * A296168 A257963 A167554

Adjacent sequences: A329280 A329281 A329282 * A329284 A329285 A329286

Keyword

nonn,cons

Author

Jianing Song, Nov 12 2019

Status

approved