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A329286 Decimal expansion of the quantile z_0.9999 of the standard normal distribution.

%I A329286 #11 Feb 16 2025 08:33:58
%S A329286 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,
%T A329286 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,
%U A329286 3,0,6,4,3,2,9,6,7,2,6,1,7,8,9,0,7,2,7,0,3,2,7
%N A329286 Decimal expansion of the quantile z_0.9999 of the standard normal distribution.
%C A329286 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.
%C A329286 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.
%H A329286 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/QuantileFunction.html">Quantile Function</a>
%H A329286 Wikipedia, <a href="https://en.wikipedia.org/wiki/Probit">Probit</a>
%e A329286 If X ~ N(0,1), then P(X<=3.7190164854...) = 0.9999, P(X<=-3.7190164854...) = 0.0001.
%o A329286 (PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.0001)*sqrt(2)
%Y A329286 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).
%K A329286 nonn,cons
%O A329286 1,1
%A A329286 _Jianing Song_, Nov 12 2019