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%I #10 Dec 14 2019 22:40:45
%S 2,3,2,6,3,4,7,8,7,4,0,4,0,8,4,1,1,0,0,8,8,5,6,0,6,1,6,3,3,4,6,9,1,1,
%T 7,2,3,3,5,1,8,1,7,1,4,1,5,3,2,0,1,3,0,6,9,0,6,5,6,4,0,2,4,7,8,9,0,8,
%U 7,6,6,2,6,4,5,6,0,3,4,4,8,7,3,5,6,8,2,2,9,3,0
%N Decimal expansion of the quantile z_0.99 of the standard normal distribution.
%C 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_0.99 (also called the 99th percentile).
%C This number can also be denoted as probit(0.99), where probit(p) is the inverse function of Phi(x). See the Wikipedia link below.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/QuantileFunction.html">Quantile Function</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Probit">Probit</a>
%e If X ~ N(0,1), then P(X<=2.3263478740...) = 0.99, P(X<=-2.3263478740...) = 0.01.
%o (PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.01)*sqrt(2)
%Y Quantiles of the standard normal distribution: A092678 (z_0.75), A329280 (z_0.9), A329281 (z_0.95), this sequence (z_0.99), A329283 (z_0.995), A329284 (z_0.999), A329285 (z_0.9995), A329286 (z_0.9999), A329287 (z_0.99999), A329363 (z_0.999999).
%K nonn,cons
%O 1,1
%A _Jianing Song_, Nov 12 2019
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