ChiSqr.h

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// Honeycomb, Copyright (C) 2015 NewGamePlus Inc.  Distributed under the Boost Software License v1.0.
#pragma once

#include "Honey/Math/Random/Dist/Gamma.h"

namespace honey
{


template<class Real>
class ChiSqr_ : public RandomDist<Real>
{
    typedef RandomDist<Real> Super;
    RandomDist_imports();
    template<class> friend class ChiSqr_;
    typedef Gaussian_<Double>   Gaussian;
    typedef Gamma_<Double>      Gamma;
    typedef GammaFunc_<Double>  GammaFunc;
    
public:
    typedef Matrix<matrix::dynamic, matrix::dynamic, Real> MatrixN;
    typedef Vec<matrix::dynamic, Real>  VecN;
    typedef Vec<2,Real>                 Vec2;

    ChiSqr_(optional<RandomGen&> gen, Real nu, Real lambda = 0)     : RandomDist<Real>(gen), nu(nu), lambda(lambda) { assert(nu > 0 && lambda >= 0); }
    ChiSqr_(Real nu, Real lambda = 0)                               : ChiSqr_(optnull, nu, lambda) {}
    
    virtual Real next() const;
    virtual Real pdf(Real x) const;
    virtual Real cdf(Real x) const;
    virtual Real cdfInv(Real P) const;
    virtual Real mean() const                           { return nu + lambda; }
    virtual Real variance() const                       { return 2*nu + 4*lambda; }
    
    Vec2 stdDevCi(Real stdDev, Real alpha) const
    {
        return Vec2(stdDev * Alge::sqrt(nu / cdfInv(1-alpha/2)),
                    stdDev * Alge::sqrt(nu / cdfInv(alpha/2)));
    }

    /*
      * A p-value below 5% is significant, meaning the observations are probably not due to random chance.
      * The degrees of freedom is assumed to be the number of observations - 1, that is,
      * none of the observations can be predicted by knowing other observations in the set.
      */ 
    static Real test(const VecN& observed, const VecN& expected);


    static Real test(const MatrixN& mat);

    Real nu;
    Real lambda;
};

typedef ChiSqr_<Real>      ChiSqr;
typedef ChiSqr_<Float>     ChiSqr_f;
typedef ChiSqr_<Double>    ChiSqr_d;

extern template class ChiSqr_<Float>;
extern template class ChiSqr_<Double>;

}