login
A329283
Decimal expansion of the quantile z_0.995 of the standard normal distribution.
8
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, 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, 5, 1, 2, 0, 7, 8, 7, 6, 4, 1, 8, 1, 1, 0, 8, 4, 9, 8, 1, 4, 6, 5, 7
OFFSET
1,1
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_0.995.
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.
LINKS
Eric Weisstein's World of Mathematics, Quantile Function
Wikipedia, Probit
EXAMPLE
If X ~ N(0,1), then P(X<=2.5758293035...) = 0.995, P(X<=-2.5758293035...) = 0.005.
PROG
(PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.005)*sqrt(2)
CROSSREFS
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).
Sequence in context: A011038 A079378 A066035 * A296168 A257963 A167554
KEYWORD
nonn,cons
AUTHOR
Jianing Song, Nov 12 2019
STATUS
approved