MoroInverseCumulativeNormal Class Reference

Moro Inverse cumulative normal distribution class. More...

#include <normaldistribution.hpp>

Collaboration diagram for MoroInverseCumulativeNormal:

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

Private Attributes
Real	average_
Real	sigma_

Static Private Attributes
static const Real	a0_ = 2.50662823884
static const Real	a1_ =-18.61500062529
static const Real	a2_ = 41.39119773534
static const Real	a3_ =-25.44106049637
static const Real	b0_ = -8.47351093090
static const Real	b1_ = 23.08336743743
static const Real	b2_ =-21.06224101826
static const Real	b3_ = 3.13082909833
static const Real	c0_ = 0.3374754822726147
static const Real	c1_ = 0.9761690190917186
static const Real	c2_ = 0.1607979714918209
static const Real	c3_ = 0.0276438810333863
static const Real	c4_ = 0.0038405729373609
static const Real	c5_ = 0.0003951896511919
static const Real	c6_ = 0.0000321767881768
static const Real	c7_ = 0.0000002888167364
static const Real	c8_ = 0.0000003960315187

Detailed Description

Moro Inverse cumulative normal distribution class.

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 uses Beasly and Springer approximation, with an improved approximation for the tails. See Boris Moro, "The Full Monte", 1995, Risk Magazine.

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.

Peter J. Acklam's approximation is better and is available as QuantLib::InverseCumulativeNormal

Definition at line 198 of file normaldistribution.hpp.

Constructor & Destructor Documentation

MoroInverseCumulativeNormal()

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

Definition at line 310 of file normaldistribution.hpp.

Member Function Documentation

operator()()

Real operator()

(

Real

x

)

const

Definition at line 140 of file normaldistribution.cpp.

Member Data Documentation

average_

Real average_

private

Definition at line 205 of file normaldistribution.hpp.

sigma_

Real sigma_

private

Definition at line 205 of file normaldistribution.hpp.

a0_

const Real a0_ = 2.50662823884

staticprivate

Definition at line 206 of file normaldistribution.hpp.

a1_

const Real a1_ =-18.61500062529

staticprivate

Definition at line 207 of file normaldistribution.hpp.

a2_

const Real a2_ = 41.39119773534

staticprivate

Definition at line 208 of file normaldistribution.hpp.

a3_

const Real a3_ =-25.44106049637

staticprivate

Definition at line 209 of file normaldistribution.hpp.

b0_

const Real b0_ = -8.47351093090

staticprivate

Definition at line 210 of file normaldistribution.hpp.

b1_

const Real b1_ = 23.08336743743

staticprivate

Definition at line 211 of file normaldistribution.hpp.

b2_

const Real b2_ =-21.06224101826

staticprivate

Definition at line 212 of file normaldistribution.hpp.

b3_

const Real b3_ = 3.13082909833

staticprivate

Definition at line 213 of file normaldistribution.hpp.

c0_

const Real c0_ = 0.3374754822726147

staticprivate

Definition at line 214 of file normaldistribution.hpp.

c1_

const Real c1_ = 0.9761690190917186

staticprivate

Definition at line 215 of file normaldistribution.hpp.

c2_

const Real c2_ = 0.1607979714918209

staticprivate

Definition at line 216 of file normaldistribution.hpp.

c3_

const Real c3_ = 0.0276438810333863

staticprivate

Definition at line 217 of file normaldistribution.hpp.

c4_

const Real c4_ = 0.0038405729373609

staticprivate

Definition at line 218 of file normaldistribution.hpp.

c5_

const Real c5_ = 0.0003951896511919

staticprivate

Definition at line 219 of file normaldistribution.hpp.

c6_

const Real c6_ = 0.0000321767881768

staticprivate

Definition at line 220 of file normaldistribution.hpp.

c7_

const Real c7_ = 0.0000002888167364

staticprivate

Definition at line 221 of file normaldistribution.hpp.

c8_

const Real c8_ = 0.0000003960315187

staticprivate

Definition at line 222 of file normaldistribution.hpp.