OFFSET
0,2
COMMENTS
Samples from a normally distributed random variable that are at least n standard deviations away from the mean have an approximately 1-in-a(n) chance of occurring.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..67
Wikipedia, 68-95-99.7 rule
FORMULA
a(n) = round( 1/erfc(n/sqrt(2)) ).
EXAMPLE
A "five-sigma" event (five standard deviations away from the mean) has a 1 in 1744278 chance of occurring. This is the requirement in particle physics for an anomaly to be recognized as a real effect, not merely a statistical fluctuation.
MATHEMATICA
Table[Round[1/Erfc[n/Sqrt[2]]], {n, 1, 16}]
PROG
(PARI) default(realprecision, 100); for(n=1, 20, print1(round(1/erfc(n/sqrt(2))), ", ")) \\ G. C. Greubel, Oct 07 2018
(Magma) [Round(1/Erfc(n/Sqrt(2))): n in [1..20]]; // G. C. Greubel, Oct 07 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeremy Tan, Jul 24 2016
EXTENSIONS
a(0)=1 prepended by Greg Huber, Jul 05 2022
STATUS
approved