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{ ******************************************************************
Inverse of Normal distribution function
Translated from C code in Cephes library (http://www.moshier.net)
****************************************************************** }
unit uinvnorm;
interface
uses
utypes, uminmax, upolev;
function InvNorm(P : Float) : Float;
{ ------------------------------------------------------------------
Inverse of Normal distribution function
Returns the argument, X, for which the area under the Gaussian
probability density function (integrated from minus infinity to X)
is equal to P.
------------------------------------------------------------------ }
implementation
function InvNorm(P : Float) : Float;
const
P0 : TabCoef = (
8.779679420055069160496E-3,
- 7.649544967784380691785E-1,
2.971493676711545292135E0,
- 4.144980036933753828858E0,
2.765359913000830285937E0,
- 9.570456817794268907847E-1,
1.659219375097958322098E-1,
- 1.140013969885358273307E-2,
0, 0);
Q0 : TabCoef = (
- 5.303846964603721860329E0,
9.908875375256718220854E0,
- 9.031318655459381388888E0,
4.496118508523213950686E0,
- 1.250016921424819972516E0,
1.823840725000038842075E-1,
- 1.088633151006419263153E-2,
0, 0, 0);
P1 : TabCoef = (
4.302849750435552180717E0,
4.360209451837096682600E1,
9.454613328844768318162E1,
9.336735653151873871756E1,
5.305046472191852391737E1,
1.775851836288460008093E1,
3.640308340137013109859E0,
3.691354900171224122390E-1,
1.403530274998072987187E-2,
1.377145111380960566197E-4);
Q1 : TabCoef = (
2.001425109170530136741E1,
7.079893963891488254284E1,
8.033277265194672063478E1,
5.034715121553662712917E1,
1.779820137342627204153E1,
3.845554944954699547539E0,
3.993627390181238962857E-1,
1.526870689522191191380E-2,
1.498700676286675466900E-4,
0);
P2 : TabCoef = (
3.244525725312906932464E0,
6.856256488128415760904E0,
3.765479340423144482796E0,
1.240893301734538935324E0,
1.740282292791367834724E-1,
9.082834200993107441750E-3,
1.617870121822776093899E-4,
7.377405643054504178605E-7,
0, 0);
Q2 : TabCoef = (
6.021509481727510630722E0,
3.528463857156936773982E0,
1.289185315656302878699E0,
1.874290142615703609510E-1,
9.867655920899636109122E-3,
1.760452434084258930442E-4,
8.028288500688538331773E-7,
0, 0, 0);
P3 : TabCoef = (
2.020331091302772535752E0,
2.133020661587413053144E0,
2.114822217898707063183E-1,
- 6.500909615246067985872E-3,
- 7.279315200737344309241E-4,
- 1.275404675610280787619E-5,
- 6.433966387613344714022E-8,
- 7.772828380948163386917E-11,
0, 0);
Q3 : TabCoef = (
2.278210997153449199574E0,
2.345321838870438196534E-1,
- 6.916708899719964982855E-3,
- 7.908542088737858288849E-4,
- 1.387652389480217178984E-5,
- 7.001476867559193780666E-8,
- 8.458494263787680376729E-11,
0, 0, 0);
var
X, Y, Z, Y2, X0, X1 : Float;
Code : Integer;
begin
if (P <= 0.0) or (P >= 1.0) then
begin
InvNorm := DefaultVal(FDomain, Sgn(P) * MaxNum);
Exit;
end;
Code := 1;
Y := P;
if Y > (1.0 - 0.13533528323661269189) then { 0.135... = exp(-2) }
begin
Y := 1.0 - Y;
Code := 0;
end;
if Y > 0.13533528323661269189 then
begin
Y := Y - 0.5;
Y2 := Y * Y;
X := Y + Y * (Y2 * PolEvl(Y2, P0, 7) / P1Evl(Y2, Q0, 7));
X := X * Sqrt2Pi;
InvNorm := X;
Exit;
end;
X := Sqrt(- 2.0 * Ln(Y));
X0 := X - Ln(X) / X;
Z := 1.0 / X;
if X < 8.0 then
X1 := Z * PolEvl(Z, P1, 9) / P1Evl(Z, Q1, 9)
else if X < 32.0 then
X1 := Z * PolEvl(Z, P2, 7) / P1Evl(Z, Q2, 7)
else
X1 := Z * PolEvl(Z, P3, 7) / P1Evl(Z, Q3, 7);
X := X0 - X1;
if Code <> 0 then
X := - X;
InvNorm := X;
end;
end.
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