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Compute the quantile function for the normal distribution. - like Excel NORMINV
/// Original C++ implementation found at http://www.wilmott.com/messageview.cfm?catid=10&threadid=38771
/// C# implementation found at http://weblogs.asp.net/esanchez/archive/2010/07/29/a-quick-and-dirty-implementation-of-excel-norminv-function-in-c.aspx
/*
* Compute the quantile function for the normal distribution.
*
* For small to moderate probabilities, algorithm referenced
* below is used to obtain an initial approximation which is
* polished with a final Newton step.
*
* For very large arguments, an algorithm of Wichura is used.
*
* REFERENCE
*
* Beasley, J. D. and S. G. Springer (1977).
* Algorithm AS 111: The percentage points of the normal distribution,
* Applied Statistics, 26, 118-121.
*
* Wichura, M.J. (1988).
* Algorithm AS 241: The Percentage Points of the Normal Distribution.
* Applied Statistics, 37, 477-484.
*/
function normsInv(p, mu, sigma)
{
if (p < 0 || p > 1)
{
throw "The probality p must be bigger than 0 and smaller than 1";
}
if (sigma < 0)
{
throw "The standard deviation sigma must be positive";
}
if (p == 0)
{
return -Infinity;
}
if (p == 1)
{
return Infinity;
}
if (sigma == 0)
{
return mu;
}
var q, r, val;
q = p - 0.5;
/*-- use AS 241 --- */
/* double ppnd16_(double *p, long *ifault)*/
/* ALGORITHM AS241 APPL. STATIST. (1988) VOL. 37, NO. 3
Produces the normal deviate Z corresponding to a given lower
tail area of P; Z is accurate to about 1 part in 10**16.
*/
if (Math.abs(q) <= .425)
{/* 0.075 <= p <= 0.925 */
r = .180625 - q * q;
val =
q * (((((((r * 2509.0809287301226727 +
33430.575583588128105) * r + 67265.770927008700853) * r +
45921.953931549871457) * r + 13731.693765509461125) * r +
1971.5909503065514427) * r + 133.14166789178437745) * r +
3.387132872796366608)
/ (((((((r * 5226.495278852854561 +
28729.085735721942674) * r + 39307.89580009271061) * r +
21213.794301586595867) * r + 5394.1960214247511077) * r +
687.1870074920579083) * r + 42.313330701600911252) * r + 1);
}
else
{ /* closer than 0.075 from {0,1} boundary */
/* r = min(p, 1-p) < 0.075 */
if (q > 0)
r = 1 - p;
else
r = p;
r = Math.Sqrt(-Math.log(r));
/* r = sqrt(-log(r)) <==> min(p, 1-p) = exp( - r^2 ) */
if (r <= 5)
{ /* <==> min(p,1-p) >= exp(-25) ~= 1.3888e-11 */
r += -1.6;
val = (((((((r * 7.7454501427834140764e-4 +
.0227238449892691845833) * r + .24178072517745061177) *
r + 1.27045825245236838258) * r +
3.64784832476320460504) * r + 5.7694972214606914055) *
r + 4.6303378461565452959) * r +
1.42343711074968357734)
/ (((((((r *
1.05075007164441684324e-9 + 5.475938084995344946e-4) *
r + .0151986665636164571966) * r +
.14810397642748007459) * r + .68976733498510000455) *
r + 1.6763848301838038494) * r +
2.05319162663775882187) * r + 1);
}
else
{ /* very close to 0 or 1 */
r += -5;
val = (((((((r * 2.01033439929228813265e-7 +
2.71155556874348757815e-5) * r +
.0012426609473880784386) * r + .026532189526576123093) *
r + .29656057182850489123) * r +
1.7848265399172913358) * r + 5.4637849111641143699) *
r + 6.6579046435011037772)
/ (((((((r *
2.04426310338993978564e-15 + 1.4215117583164458887e-7) *
r + 1.8463183175100546818e-5) * r +
7.868691311456132591e-4) * r + .0148753612908506148525)
* r + .13692988092273580531) * r +
.59983220655588793769) * r + 1);
}
if (q < 0.0)
{
val = -val;
}
}
return mu + sigma * val;
}
// normInv(0.2, 3.5, 0,707106781);
@michael-simons

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commented Feb 21, 2013

@itainoam

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commented Jul 2, 2015

Thanks for your work!
There's a typing error in this example that prevents it from running. Row 81: replace Math.Sqrt with Math.sqrt

@jamiezhang

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commented Dec 1, 2015

// normInv(0.2, 3.5, 0,707106781);
A minor thing: the last number has a comma while it should be a dot?

@bor2com

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commented Feb 4, 2016

It's Math.sqrtnot Math.Sqrt. Thank you for the snippet.

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