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A329286
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Decimal expansion of the quantile z_0.9999 of the standard normal distribution.
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8
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3, 7, 1, 9, 0, 1, 6, 4, 8, 5, 4, 5, 5, 6, 8, 0, 5, 6, 4, 3, 9, 3, 6, 6, 0, 6, 2, 4, 5, 0, 8, 4, 7, 8, 3, 0, 4, 6, 1, 7, 3, 1, 9, 7, 0, 8, 2, 7, 2, 1, 5, 4, 6, 8, 4, 7, 3, 9, 4, 8, 1, 7, 2, 4, 7, 8, 6, 9, 3, 0, 6, 4, 3, 2, 9, 6, 7, 2, 6, 1, 7, 8, 9, 0, 7, 2, 7, 0, 3, 2, 7
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OFFSET
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1,1
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COMMENTS
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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_0.9999.
This number can also be denoted as probit(0.9999), where probit(p) is the inverse function of Phi(x). See the Wikipedia link below.
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LINKS
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EXAMPLE
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If X ~ N(0,1), then P(X<=3.7190164854...) = 0.9999, P(X<=-3.7190164854...) = 0.0001.
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PROG
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(PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.0001)*sqrt(2)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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