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chisquaredistr.pas
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144 lines (102 loc) · 4.59 KB
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{$MODESWITCH RESULT+}
{$GOTO ON}
(*************************************************************************
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
Contributors:
* Sergey Bochkanov (ALGLIB project). Translation from C to
pseudocode.
See subroutines comments for additional copyrights.
>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************)
unit chisquaredistr;
interface
uses Math, Sysutils, Ap, gammafunc, normaldistr, igammaf;
function ChiSquareDistribution(v : Double; x : Double):Double;
function ChiSquareCDistribution(v : Double; x : Double):Double;
function InvChiSquareDistribution(v : Double; y : Double):Double;
implementation
(*************************************************************************
Chi-square distribution
Returns the area under the left hand tail (from 0 to x)
of the Chi square probability density function with
v degrees of freedom.
x
-
1 | | v/2-1 -t/2
P( x | v ) = ----------- | t e dt
v/2 - | |
2 | (v/2) -
0
where x is the Chi-square variable.
The incomplete gamma integral is used, according to the
formula
y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
The arguments must both be positive.
ACCURACY:
See incomplete gamma function
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
*************************************************************************)
function ChiSquareDistribution(v : Double; x : Double):Double;
begin
Assert(AP_FP_Greater_Eq(x,0) and AP_FP_Greater_Eq(v,1), 'Domain error in ChiSquareDistribution');
Result := IncompleteGamma(v/Double(2.0), x/Double(2.0));
end;
(*************************************************************************
Complemented Chi-square distribution
Returns the area under the right hand tail (from x to
infinity) of the Chi square probability density function
with v degrees of freedom:
inf.
-
1 | | v/2-1 -t/2
P( x | v ) = ----------- | t e dt
v/2 - | |
2 | (v/2) -
x
where x is the Chi-square variable.
The incomplete gamma integral is used, according to the
formula
y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
The arguments must both be positive.
ACCURACY:
See incomplete gamma function
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
*************************************************************************)
function ChiSquareCDistribution(v : Double; x : Double):Double;
begin
Assert(AP_FP_Greater_Eq(x,0) and AP_FP_Greater_Eq(v,1), 'Domain error in ChiSquareDistributionC');
Result := IncompleteGammaC(v/Double(2.0), x/Double(2.0));
end;
(*************************************************************************
Inverse of complemented Chi-square distribution
Finds the Chi-square argument x such that the integral
from x to infinity of the Chi-square density is equal
to the given cumulative probability y.
This is accomplished using the inverse gamma integral
function and the relation
x/2 = igami( df/2, y );
ACCURACY:
See inverse incomplete gamma function
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
*************************************************************************)
function InvChiSquareDistribution(v : Double; y : Double):Double;
begin
Assert(AP_FP_Greater_Eq(y,0) and AP_FP_Less_Eq(y,1) and AP_FP_Greater_Eq(v,1), 'Domain error in InvChiSquareDistribution');
Result := 2*InvIncompleteGammaC(Double(0.5)*v, y);
end;
end.