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A329281 Decimal expansion of the quantile z_0.95 of the standard normal distribution. 8


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

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

%U 0,6,3,5,1,9,9,4,4,6,7,4,1,7,6,6,4,8,7,8,4,8,5

%N Decimal expansion of the quantile z_0.95 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_0.95 (also called the 95th percentile).

%C This number can also be denoted as probit(0.95), 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<=1.6448536269...) = 0.95, P(X<=-1.6448536269...) = 0.05.

%o (PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.05)*sqrt(2)

%Y Quantiles of the standard normal distribution: A092678 (z_0.75), A329280 (z_0.9), this sequence (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), A329363 (z_0.999999).

%K nonn,cons

%O 1,2

%A _Jianing Song_, Nov 12 2019

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Last modified April 6 21:24 EDT 2020. Contains 333286 sequences. (Running on oeis4.)