InverseCumulativeNormal Class Reference

Inverse cumulative normal distribution function. More...

#include <normaldistribution.hpp>

Collaboration diagram for InverseCumulativeNormal:

Public Member Functions
	InverseCumulativeNormal (Real average=0.0, Real sigma=1.0)
Real	operator() (Real x) const

Static Public Member Functions
static Real	standard_value (Real x)

Static Private Member Functions
static Real	tail_value (Real x)

Private Attributes
Real	average_
Real	sigma_

Static Private Attributes
static const CumulativeNormalDistribution	f_
static const Real	a1_ = -3.969683028665376e+01
static const Real	a2_ = 2.209460984245205e+02
static const Real	a3_ = -2.759285104469687e+02
static const Real	a4_ = 1.383577518672690e+02
static const Real	a5_ = -3.066479806614716e+01
static const Real	a6_ = 2.506628277459239e+00
static const Real	b1_ = -5.447609879822406e+01
static const Real	b2_ = 1.615858368580409e+02
static const Real	b3_ = -1.556989798598866e+02
static const Real	b4_ = 6.680131188771972e+01
static const Real	b5_ = -1.328068155288572e+01
static const Real	c1_ = -7.784894002430293e-03
static const Real	c2_ = -3.223964580411365e-01
static const Real	c3_ = -2.400758277161838e+00
static const Real	c4_ = -2.549732539343734e+00
static const Real	c5_ = 4.374664141464968e+00
static const Real	c6_ = 2.938163982698783e+00
static const Real	d1_ = 7.784695709041462e-03
static const Real	d2_ = 3.224671290700398e-01
static const Real	d3_ = 2.445134137142996e+00
static const Real	d4_ = 3.754408661907416e+00
static const Real	x_low_ = 0.02425
static const Real	x_high_ = 1.0 - x_low_

Detailed Description

Inverse cumulative normal distribution function.

Given x between zero and one as the integral value of a gaussian normal distribution this class provides the value y such that formula here ...

It use Acklam's approximation: by Peter J. Acklam, University of Oslo, Statistics Division. URL: http://home.online.no/~pjacklam/notes/invnorm/index.html

This class can also be used to generate a gaussian normal distribution from a uniform distribution. This is especially useful when a gaussian normal distribution is generated from a low discrepancy uniform distribution: in this case the traditional Box-Muller approach and its variants would not preserve the sequence's low-discrepancy.

Definition at line 100 of file normaldistribution.hpp.

Constructor & Destructor Documentation

InverseCumulativeNormal()

InverseCumulativeNormal	(	Real	average = 0.0,
		Real	sigma = 1.0
	)

Definition at line 301 of file normaldistribution.hpp.

Member Function Documentation

operator()()

Real operator()

(

Real

x

)

const

Definition at line 105 of file normaldistribution.hpp.

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standard_value()

static Real standard_value ( Real  x )

static

Definition at line 113 of file normaldistribution.hpp.

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tail_value()

Real tail_value ( Real  x )

staticprivate

Definition at line 91 of file normaldistribution.cpp.

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Member Data Documentation

f_

const CumulativeNormalDistribution f_

staticprivate

Definition at line 147 of file normaldistribution.hpp.

average_

Real average_

private

Definition at line 149 of file normaldistribution.hpp.

sigma_

Real sigma_

private

Definition at line 149 of file normaldistribution.hpp.

a1_

const Real a1_ = -3.969683028665376e+01

staticprivate

Definition at line 150 of file normaldistribution.hpp.

a2_

const Real a2_ = 2.209460984245205e+02

staticprivate

Definition at line 151 of file normaldistribution.hpp.

a3_

const Real a3_ = -2.759285104469687e+02

staticprivate

Definition at line 152 of file normaldistribution.hpp.

a4_

const Real a4_ = 1.383577518672690e+02

staticprivate

Definition at line 153 of file normaldistribution.hpp.

a5_

const Real a5_ = -3.066479806614716e+01

staticprivate

Definition at line 154 of file normaldistribution.hpp.

a6_

const Real a6_ = 2.506628277459239e+00

staticprivate

Definition at line 155 of file normaldistribution.hpp.

b1_

const Real b1_ = -5.447609879822406e+01

staticprivate

Definition at line 156 of file normaldistribution.hpp.

b2_

const Real b2_ = 1.615858368580409e+02

staticprivate

Definition at line 157 of file normaldistribution.hpp.

b3_

const Real b3_ = -1.556989798598866e+02

staticprivate

Definition at line 158 of file normaldistribution.hpp.

b4_

const Real b4_ = 6.680131188771972e+01

staticprivate

Definition at line 159 of file normaldistribution.hpp.

b5_

const Real b5_ = -1.328068155288572e+01

staticprivate

Definition at line 160 of file normaldistribution.hpp.

c1_

const Real c1_ = -7.784894002430293e-03

staticprivate

Definition at line 161 of file normaldistribution.hpp.

c2_

const Real c2_ = -3.223964580411365e-01

staticprivate

Definition at line 162 of file normaldistribution.hpp.

c3_

const Real c3_ = -2.400758277161838e+00

staticprivate

Definition at line 163 of file normaldistribution.hpp.

c4_

const Real c4_ = -2.549732539343734e+00

staticprivate

Definition at line 164 of file normaldistribution.hpp.

c5_

const Real c5_ = 4.374664141464968e+00

staticprivate

Definition at line 165 of file normaldistribution.hpp.

c6_

const Real c6_ = 2.938163982698783e+00

staticprivate

Definition at line 166 of file normaldistribution.hpp.

d1_

const Real d1_ = 7.784695709041462e-03

staticprivate

Definition at line 167 of file normaldistribution.hpp.

d2_

const Real d2_ = 3.224671290700398e-01

staticprivate

Definition at line 168 of file normaldistribution.hpp.

d3_

const Real d3_ = 2.445134137142996e+00

staticprivate

Definition at line 169 of file normaldistribution.hpp.

d4_

const Real d4_ = 3.754408661907416e+00

staticprivate

Definition at line 170 of file normaldistribution.hpp.

x_low_

const Real x_low_ = 0.02425

staticprivate

Definition at line 171 of file normaldistribution.hpp.

x_high_

const Real x_high_ = 1.0 - x_low_

staticprivate

Definition at line 172 of file normaldistribution.hpp.