login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A329363 Decimal expansion of the quantile z_0.999999 of the standard normal distribution. 8
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, 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, 1, 1, 6, 5, 3, 6, 0, 0, 1, 8, 4, 3, 4, 8, 5, 2, 8, 5, 1, 6, 4, 5, 5 (list; constant; graph; refs; listen; history; text; internal format)
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_0.999999.

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.

LINKS

Table of n, a(n) for n=1..91.

Eric Weisstein's World of Mathematics, Quantile Function

Wikipedia, Probit

EXAMPLE

If X ~ N(0,1), then P(X<=4.7534243088...) = 0.999999, P(X<=-4.7534243088...) = 0.000001.

PROG

(PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.000001)*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), 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).

Sequence in context: A011518 A132265 A175348 * A079356 A146539 A322580

Adjacent sequences:  A329360 A329361 A329362 * A329364 A329365 A329366

KEYWORD

nonn,cons

AUTHOR

Jianing Song, Nov 12 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 8 04:26 EDT 2020. Contains 333312 sequences. (Running on oeis4.)