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A329283 Decimal expansion of the quantile z_0.995 of the standard normal distribution.

%I A329283 #11 Feb 16 2025 08:33:58
%S A329283 2,5,7,5,8,2,9,3,0,3,5,4,8,9,0,0,7,6,0,9,7,8,5,7,6,7,4,8,6,0,3,8,1,4,
%T A329283 1,1,7,3,0,6,0,1,7,6,3,4,2,7,6,3,1,7,3,7,6,4,6,0,4,8,6,2,1,8,8,6,2,5,
%U A329283 5,1,2,0,7,8,7,6,4,1,8,1,1,0,8,4,9,8,1,4,6,5,7
%N A329283 Decimal expansion of the quantile z_0.995 of the standard normal distribution.
%C A329283 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_0.995.
%C A329283 This number can also be denoted as probit(0.995), where probit(p) is the inverse function of Phi(x). See the Wikipedia link below.
%H A329283 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/QuantileFunction.html">Quantile Function</a>
%H A329283 Wikipedia, <a href="https://en.wikipedia.org/wiki/Probit">Probit</a>
%e A329283 If X ~ N(0,1), then P(X<=2.5758293035...) = 0.995, P(X<=-2.5758293035...) = 0.005.
%o A329283 (PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.005)*sqrt(2)
%Y A329283 Quantiles of the standard normal distribution: A092678 (z_0.75), A329280 (z_0.9), A329281 (z_0.95), A329282 (z_0.99), this sequence (z_0.995), A329284 (z_0.999), A329285 (z_0.9995), A329286 (z_0.9999), A329287 (z_0.99999), A329363 (z_0.999999).
%K A329283 nonn,cons
%O A329283 1,1
%A A329283 _Jianing Song_, Nov 12 2019