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A329363 Decimal expansion of the quantile z_0.999999 of the standard normal distribution. 8

%I #7 Dec 14 2019 22:37:37

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

%T 0,0,5,6,4,2,2,3,3,7,2,6,8,2,7,0,2,7,6,7,8,6,6,3,1,2,7,2,3,7,1,1,7,4,

%U 1,1,6,5,3,6,0,0,1,8,4,3,4,8,5,2,8,5,1,6,4,5,5

%N Decimal expansion of the quantile z_0.999999 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_0.999999.

%C This number can also be denoted as probit(0.999999), 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<=4.7534243088...) = 0.999999, P(X<=-4.7534243088...) = 0.000001.

%o (PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.000001)*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), A329285 (z_0.9995), A329286 (z_0.9999), A329287 (z_0.99999), this sequence (z_0.999999).

%K nonn,cons

%O 1,1

%A _Jianing Song_, Nov 12 2019

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Last modified March 28 14:13 EDT 2024. Contains 371254 sequences. (Running on oeis4.)