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A329284 Decimal expansion of the quantile z_0.999 of the standard normal distribution. 8
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 (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_0.999.

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

AUTHOR

Jianing Song, Nov 12 2019

STATUS

approved

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Last modified April 5 03:15 EDT 2020. Contains 333238 sequences. (Running on oeis4.)