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A329287 Decimal expansion of the quantile z_0.99999 of the standard normal distribution.

%I A329287 #12 Feb 16 2025 08:33:58
%S A329287 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,
%T A329287 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,
%U A329287 3,6,8,9,7,0,4,0,3,7,9,5,5,1,5,6,3,3,7,3,4,1,4
%N A329287 Decimal expansion of the quantile z_0.99999 of the standard normal distribution.
%C A329287 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.
%C A329287 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.
%H A329287 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/QuantileFunction.html">Quantile Function</a>
%H A329287 Wikipedia, <a href="https://en.wikipedia.org/wiki/Probit">Probit</a>
%e A329287 If X ~ N(0,1), then P(X<=4.2648907939...) = 0.99999, P(X<=-4.2648907939...) = 0.00001.
%o A329287 (PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.00001)*sqrt(2)
%Y A329287 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).
%K A329287 nonn,cons
%O A329287 1,1
%A A329287 _Jianing Song_, Nov 12 2019