/usr/include/openturns/DistFunc.hxx is in libopenturns-dev 1.9-5.
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/**
* @brief OpenTURNS wrapper to a library of special functions
*
* Copyright 2005-2017 Airbus-EDF-IMACS-Phimeca
*
* This library is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This library 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* along with this library. If not, see <http://www.gnu.org/licenses/>.
*
*/
#ifndef OPENTURNS_DISTFUNC_HXX
#define OPENTURNS_DISTFUNC_HXX
#include "openturns/OTprivate.hxx"
#include "openturns/ResourceMap.hxx"
#include "openturns/Point.hxx"
#include "openturns/Indices.hxx"
#include "openturns/Sample.hxx"
BEGIN_NAMESPACE_OPENTURNS
class OT_API DistFunc
{
public:
static const UnsignedInteger NumberOfBandNormalZigurrat;
static const Scalar NormalZigguratTail;
// The array NormalZigguratAbscissa stores the abscissas of the bands:
// the ith band is [NormalZigguratAbscissa[0], NormalZigguratAbscissa[i+1]] with
// NormalZigguratAbscissa[0] = 0.0 and
// NormalZigguratAbscissa[NumberOfBandNormalZigurrat] = NormalZigguratTail
static const Scalar NormalZigguratAbscissa[];
// The array NormalZigguratRatio stores the ratio between a band and the next one,
// starting from the smallest one:
// NormalZigguratRatio[i] = NormalZigguratAbscissa[i] / NormalZigguratAbscissa[i+1]
static const Scalar NormalZigguratRatio[];
// For Beta distribution. WARNING: here we adopt the classical definition
// If tail=false, compute P(X<=x), else P(X>x)
static Scalar pBeta(const Scalar p1,
const Scalar p2,
const Scalar x,
const Bool tail = false);
// If tail=false, compute x such that P(X<=x)=q, else x such that P(X>x)=q
static Scalar qBeta(const Scalar p1,
const Scalar p2,
const Scalar p,
const Bool tail = false);
static Scalar rBeta(const Scalar p1,
const Scalar p2);
static Point rBeta(const Scalar p1,
const Scalar p2,
const UnsignedInteger size);
// For the Binomial distribution
private:
static Scalar fcBinomial(const UnsignedInteger k);
public:
static UnsignedInteger rBinomial(const UnsignedInteger n,
const Scalar p);
static Indices rBinomial(const UnsignedInteger n,
const Scalar p,
const UnsignedInteger size);
// For Gamma distribution
static Scalar pGamma(const Scalar k,
const Scalar x,
const Bool tail = false);
static Scalar qGamma(const Scalar k,
const Scalar p,
const Bool tail = false);
static Scalar rGamma(const Scalar k);
static Point rGamma(const Scalar k,
const UnsignedInteger size);
// For Kolmogorov distribution
static Scalar pKolmogorov(const UnsignedInteger n,
const Scalar x,
const Bool tail = false);
// For NonCentralChiSquare distribution
static Scalar dNonCentralChiSquare(const Scalar nu,
const Scalar lambda,
const Scalar x,
const Scalar precision = ResourceMap::GetAsScalar("DistFunc-Precision"),
const UnsignedInteger maximumIteration = ResourceMap::GetAsScalar("DistFunc-MaximumIteration"));
static Scalar pNonCentralChiSquare(const Scalar nu,
const Scalar lambda,
const Scalar x,
const Bool tail = false,
const Scalar precision = ResourceMap::GetAsScalar("DistFunc-Precision"),
const UnsignedInteger maximumIteration = ResourceMap::GetAsScalar("DistFunc-MaximumIteration"));
static Scalar rNonCentralChiSquare(const Scalar nu,
const Scalar lambda);
static Point rNonCentralChiSquare(const Scalar nu,
const Scalar lambda,
const UnsignedInteger size);
// For NonCentralStudent distribution
static Scalar dNonCentralStudent(const Scalar nu,
const Scalar delta,
const Scalar x);
static Scalar dNonCentralStudentAlt0(const Scalar nu,
const Scalar delta,
const Scalar x,
const Scalar precision = ResourceMap::GetAsScalar("DistFunc-Precision"),
const UnsignedInteger maximumIteration = ResourceMap::GetAsScalar("DistFunc-MaximumIteration"));
static Scalar pNonCentralStudent(const Scalar nu,
const Scalar delta,
const Scalar x,
const Bool tail = false);
static Scalar rNonCentralStudent(const Scalar nu,
const Scalar delta);
static Point rNonCentralStudent(const Scalar nu,
const Scalar delta,
const UnsignedInteger size);
// For Normal distribution
static Scalar pNormal(const Scalar x,
const Bool tail = false);
static Scalar pNormal2D(const Scalar x1,
const Scalar x2,
const Scalar rho,
const Bool tail = false);
static Scalar pNormal3D(const Scalar x1,
const Scalar x2,
const Scalar x3,
const Scalar rho12,
const Scalar rho13,
const Scalar rho23,
const Bool tail = false);
static Scalar qNormal(const Scalar p,
const Bool tail = false);
static Scalar rNormal();
static Point rNormal(const UnsignedInteger size);
// For Poisson distribution
static Scalar qPoisson(const Scalar lambda,
const Scalar p,
const Bool tail = false);
static UnsignedInteger rPoisson(const Scalar lambda);
static Indices rPoisson(const Scalar lambda,
const UnsignedInteger size);
// For Student distribution
static Scalar pStudent(const Scalar nu,
const Scalar x,
const Bool tail = false);
static Scalar qStudent(const Scalar nu,
const Scalar p,
const Bool tail = false);
static Scalar rStudent(const Scalar nu);
static Point rStudent(const Scalar nu,
const UnsignedInteger size);
static Point rUniformTriangle(const Point & a,
const Point & b,
const Point & c);
static Sample rUniformTriangle(const Point & a,
const Point & b,
const Point & c,
const UnsignedInteger size);
// For TruncatedNormal distribution
// static Scalar rTruncatedNormal(const Scalar a, const Scalar b);
// Compute the expectation of the min of n independent standard normal random variables
static Scalar eZ1(const UnsignedInteger n);
// K factor for exact two-sided tolerance intervals of normal pooled populations
static Scalar kFactorPooled(const UnsignedInteger n,
const UnsignedInteger m,
const Scalar p,
const Scalar alpha);
// K factor for exact two-sided tolerance intervals of a normal population
static Scalar kFactor(const UnsignedInteger n,
const Scalar p,
const Scalar alpha);
// Asymptotic distribution of the DickeyFuller distribution
static Scalar pDickeyFullerTrend(const Scalar x,
const Bool tail = false);
static Scalar pDickeyFullerConstant(const Scalar x,
const Bool tail = false);
static Scalar pDickeyFullerNoConstant(const Scalar x,
const Bool tail = false);
static Scalar qDickeyFullerTrend(const Scalar p,
const Bool tail = false);
static Scalar qDickeyFullerConstant(const Scalar p,
const Bool tail = false);
static Scalar qDickeyFullerNoConstant(const Scalar p,
const Bool tail = false);
}; /* class DistFunc */
END_NAMESPACE_OPENTURNS
#endif /* OPENTURNS_DISTFUNC_HXX */
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