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A329286
Decimal expansion of the quantile z_0.9999 of the standard normal distribution.
8
3, 7, 1, 9, 0, 1, 6, 4, 8, 5, 4, 5, 5, 6, 8, 0, 5, 6, 4, 3, 9, 3, 6, 6, 0, 6, 2, 4, 5, 0, 8, 4, 7, 8, 3, 0, 4, 6, 1, 7, 3, 1, 9, 7, 0, 8, 2, 7, 2, 1, 5, 4, 6, 8, 4, 7, 3, 9, 4, 8, 1, 7, 2, 4, 7, 8, 6, 9, 3, 0, 6, 4, 3, 2, 9, 6, 7, 2, 6, 1, 7, 8, 9, 0, 7, 2, 7, 0, 3, 2, 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_0.9999.
This number can also be denoted as probit(0.9999), where probit(p) is the inverse function of Phi(x). See the Wikipedia link below.
LINKS
Eric Weisstein's World of Mathematics, Quantile Function
Wikipedia, Probit
EXAMPLE
If X ~ N(0,1), then P(X<=3.7190164854...) = 0.9999, P(X<=-3.7190164854...) = 0.0001.
PROG
(PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.0001)*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), this sequence (z_0.9999), A329287 (z_0.99999), A329363 (z_0.999999).
Sequence in context: A291858 A355417 A137989 * A191335 A338366 A124138
KEYWORD
nonn,cons
AUTHOR
Jianing Song, Nov 12 2019
STATUS
approved