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A329287 Decimal expansion of the quantile z_0.99999 of the standard normal distribution. 8
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 (list; constant; graph; refs; listen; history; text; internal format)
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.

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 * A021705 A228084 A188941

Adjacent sequences:  A329284 A329285 A329286 * A329288 A329289 A329290

KEYWORD

nonn,cons

AUTHOR

Jianing Song, Nov 12 2019

STATUS

approved

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Last modified April 9 06:59 EDT 2020. Contains 333344 sequences. (Running on oeis4.)