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A329285 Decimal expansion of the quantile z_0.9995 of the standard normal distribution. 8
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 (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_0.9995.

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 A060481 A228492

Adjacent sequences:  A329282 A329283 A329284 * A329286 A329287 A329288

KEYWORD

nonn,cons

AUTHOR

Jianing Song, Nov 12 2019

STATUS

approved

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)