login
A329280
Decimal expansion of the quantile z_0.9 of the standard normal distribution.
8
1, 2, 8, 1, 5, 5, 1, 5, 6, 5, 5, 4, 4, 6, 0, 0, 4, 6, 6, 9, 6, 5, 1, 0, 3, 3, 2, 9, 4, 4, 8, 7, 4, 2, 8, 1, 8, 6, 1, 9, 9, 0, 7, 8, 2, 4, 3, 5, 2, 5, 8, 2, 6, 5, 9, 7, 0, 2, 6, 4, 8, 2, 3, 0, 5, 6, 5, 7, 0, 3, 3, 2, 4, 8, 1, 2, 2, 4, 5, 4, 3, 0, 1, 5, 5, 4, 3, 8, 1, 6, 1
OFFSET
1,2
COMMENTS
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_0.9 (also called the 9th decile or the 90th percentile).
This number can also be denoted as probit(0.9), where probit(p) is the inverse function of Phi(x). See the Wikipedia link below.
LINKS
Eric Weisstein's World of Mathematics, Quantile Function
Wikipedia, Probit
FORMULA
If X ~ N(0,1), then P(X<=1.2815515655...) = 0.9, P(X<=-1.2815515655...) = 0.1.
MATHEMATICA
RealDigits[Sqrt[2] InverseErfc[9/10], 10, 100][[1]] (* Jean-François Alcover, Sep 26 2020 *)
PROG
(PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.1)*sqrt(2)
CROSSREFS
Quantiles of the standard normal distribution: A092678 (z_0.75), this sequence (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), A329363 (z_0.999999).
Sequence in context: A156029 A333476 A120026 * A109089 A200479 A198873
KEYWORD
nonn,cons
AUTHOR
Jianing Song, Nov 12 2019
STATUS
approved