# Boost C++ Libraries

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### boost/random/non_central_chi_squared_distribution.hpp

/* boost random/non_central_chi_squared_distribution.hpp header file
*
* Copyright Thijs van den Berg 2014
*
* accompanying file LICENSE_1_0.txt or copy at
*
*
* $Id$
*/

#ifndef BOOST_RANDOM_NON_CENTRAL_CHI_SQUARED_DISTRIBUTION_HPP
#define BOOST_RANDOM_NON_CENTRAL_CHI_SQUARED_DISTRIBUTION_HPP

#include <boost/config/no_tr1/cmath.hpp>
#include <iosfwd>
#include <istream>
#include <boost/limits.hpp>
#include <boost/random/detail/config.hpp>
#include <boost/random/detail/operators.hpp>
#include <boost/random/uniform_real_distribution.hpp>
#include <boost/random/normal_distribution.hpp>
#include <boost/random/chi_squared_distribution.hpp>
#include <boost/random/poisson_distribution.hpp>

namespace boost {
namespace random {

/**
* The noncentral chi-squared distribution is a real valued distribution with
* two parameter, @c k and @c lambda.  The distribution produces values > 0.
*
* This is the distribution of the sum of squares of k Normal distributed
* variates each with variance one and \f$\lambda\f$ the sum of squares of the
* normal means.
*
* The distribution function is
* \f$\displaystyle P(x) = \frac{1}{2} e^{-(x+\lambda)/2} \left( \frac{x}{\lambda} \right)^{k/4-1/2} I_{k/2-1}( \sqrt{\lambda x} )\f$.
*  where  \f$\displaystyle I_\nu(z)\f$ is a modified Bessel function of the
* first kind.
*
* The algorithm is taken from
*
*  @blockquote
*  "Monte Carlo Methods in Financial Engineering", Paul Glasserman,
*  2003, XIII, 596 p, Stochastic Modelling and Applied Probability, Vol. 53,
*  ISBN 978-0-387-21617-1, p 124, Fig. 3.5.
*  @endblockquote
*/
template <typename RealType = double>
class non_central_chi_squared_distribution {
public:
typedef RealType result_type;
typedef RealType input_type;

class param_type {
public:
typedef non_central_chi_squared_distribution distribution_type;

/**
* Constructs the parameters of a non_central_chi_squared_distribution.
* @c k and @c lambda are the parameter of the distribution.
*
* Requires: k > 0 && lambda > 0
*/
explicit
param_type(RealType k_arg = RealType(1), RealType lambda_arg = RealType(1))
: _k(k_arg), _lambda(lambda_arg)
{
BOOST_ASSERT(k_arg > RealType(0));
BOOST_ASSERT(lambda_arg > RealType(0));
}

/** Returns the @c k parameter of the distribution */
RealType k() const { return _k; }

/** Returns the @c lambda parameter of the distribution */
RealType lambda() const { return _lambda; }

/** Writes the parameters of the distribution to a @c std::ostream. */
BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm)
{
os << parm._k << ' ' << parm._lambda;
return os;
}

/** Reads the parameters of the distribution from a @c std::istream. */
BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm)
{
is >> parm._k >> std::ws >> parm._lambda;
return is;
}

/** Returns true if the parameters have the same values. */
BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
{ return lhs._k == rhs._k && lhs._lambda == rhs._lambda; }

/** Returns true if the parameters have different values. */
BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)

private:
RealType _k;
RealType _lambda;
};

/**
* Construct a @c non_central_chi_squared_distribution object. @c k and
* @c lambda are the parameter of the distribution.
*
* Requires: k > 0 && lambda > 0
*/
explicit
non_central_chi_squared_distribution(RealType k_arg = RealType(1), RealType lambda_arg = RealType(1))
: _param(k_arg, lambda_arg)
{
BOOST_ASSERT(k_arg > RealType(0));
BOOST_ASSERT(lambda_arg > RealType(0));
}

/**
* Construct a @c non_central_chi_squared_distribution object from the parameter.
*/
explicit
non_central_chi_squared_distribution(const param_type& parm)
: _param( parm )
{ }

/**
* Returns a random variate distributed according to the
* non central chi squared distribution specified by @c param.
*/
template<typename URNG>
RealType operator()(URNG& eng, const param_type& parm) const
{ return non_central_chi_squared_distribution(parm)(eng); }

/**
* Returns a random variate distributed according to the
* non central chi squared distribution.
*/
template<typename URNG>
RealType operator()(URNG& eng)
{
using std::sqrt;
if (_param.k() > 1) {
boost::random::normal_distribution<RealType> n_dist;
boost::random::chi_squared_distribution<RealType> c_dist(_param.k() - RealType(1));
RealType _z = n_dist(eng);
RealType _x = c_dist(eng);
RealType term1 = _z + sqrt(_param.lambda());
return term1*term1 + _x;
}
else {
boost::random::poisson_distribution<> p_dist(_param.lambda()/RealType(2));
boost::random::poisson_distribution<>::result_type _p = p_dist(eng);
boost::random::chi_squared_distribution<RealType> c_dist(_param.k() + RealType(2)*_p);
return c_dist(eng);
}
}

/** Returns the @c k parameter of the distribution. */
RealType k() const { return _param.k(); }

/** Returns the @c lambda parameter of the distribution. */
RealType lambda() const { return _param.lambda(); }

/** Returns the parameters of the distribution. */
param_type param() const { return _param; }

/** Sets parameters of the distribution. */
void param(const param_type& parm) { _param = parm; }

/** Resets the distribution, so that subsequent uses does not depend on values already produced by it.*/
void reset() {}

/** Returns the smallest value that the distribution can produce. */
RealType min BOOST_PREVENT_MACRO_SUBSTITUTION() const
{ return RealType(0); }

/** Returns the largest value that the distribution can produce. */
RealType max BOOST_PREVENT_MACRO_SUBSTITUTION() const
{ return (std::numeric_limits<RealType>::infinity)(); }

/** Writes the parameters of the distribution to a @c std::ostream. */
BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, non_central_chi_squared_distribution, dist)
{
os << dist.param();
return os;
}

/** reads the parameters of the distribution from a @c std::istream. */
BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, non_central_chi_squared_distribution, dist)
{
param_type parm;
if(is >> parm) {
dist.param(parm);
}
return is;
}

/** Returns true if two distributions have the same parameters and produce
the same sequence of random numbers given equal generators.*/
BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(non_central_chi_squared_distribution, lhs, rhs)
{ return lhs.param() == rhs.param(); }

/** Returns true if two distributions have different parameters and/or can produce
different sequences of random numbers given equal generators.*/
BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(non_central_chi_squared_distribution)

private:

/// @cond show_private
param_type  _param;
/// @endcond
};

} // namespace random
} // namespace boost

#endif