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A329285 Decimal expansion of the quantile z_0.9995 of the standard normal distribution. 8

%I #10 Dec 14 2019 22:38:58

%S 3,2,9,0,5,2,6,7,3,1,4,9,1,8,9,4,7,9,3,2,2,1,6,2,7,0,3,5,3,7,4,6,4,9,

%T 1,7,9,2,1,6,2,2,6,9,2,5,6,7,7,3,9,0,0,7,6,9,9,3,8,7,8,2,8,6,9,1,7,9,

%U 9,6,5,9,9,6,4,9,7,5,7,8,6,4,2,1,1,7,4,4,7,0,8

%N Decimal expansion of the quantile z_0.9995 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_0.9995.

%C This number can also be denoted as probit(0.9995), 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<=3.2905267314...) = 0.9995, P(X<=-3.2905267314...) = 0.0005.

%o (PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.0005)*sqrt(2)

%Y 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), this sequence (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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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)