/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*

 Copyright (C) 2008 Roland Lichters

 This file is part of QuantLib, a free-software/open-source library

 for financial quantitative analysts and developers - http://quantlib.org/

 QuantLib is free software: you can redistribute it and/or modify it

 under the terms of the QuantLib license.  You should have received a

 copy of the license along with this program; if not, please email

 <quantlib-dev@lists.sf.net>. The license is also available online at

 <https://www.quantlib.org/license.shtml>.

 This program 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 license for more details.

*/

/*! \file studenttdistribution.hpp

    \brief Student's t-distribution

*/

#ifndef quantlib_student_t_distribution_hpp

#define quantlib_student_t_distribution_hpp

#include <ql/errors.hpp>

#include <ql/types.hpp>

#include <functional>

namespace QuantLib {

    //! Student t-distribution

    /*! Probability density function for \f$ n \f$ degrees of freedom

        (see mathworld.wolfram.com or wikipedia.org):

        \f[

        f(x) = \frac {\Gamma\left(\frac{n+1}{2}\right)} {\sqrt{n\pi}

        \, \Gamma\left(\frac{n}{2}\right)}\:

        \frac {1} {\left(1+\frac{x^2}{n}\right)^{(n+1)/2}}

        \f]

    */

    class StudentDistribution {

      public:

        StudentDistribution(Integer n) : n_(n) {

            QL_REQUIRE(n > 0, "invalid parameter for t-distribution");

        }

        Real operator()(Real x) const;

      private:

        Integer n_;

    };

    //! Cumulative Student t-distribution

    /*! Cumulative distribution function for \f$ n \f$ degrees of freedom

        (see mathworld.wolfram.com):

        \f[

        F(x) = \int_{-\infty}^x\,f(y)\,dy

        = \frac{1}{2}\,

        +\,\frac{1}{2}\,sgn(x)\,

        \left[ I\left(1,\frac{n}{2},\frac{1}{2}\right)

        - I\left(\frac{n}{n+y^2}, \frac{n}{2},\frac{1}{2}\right)\right]

        \f]

        where \f$ I(z; a, b) \f$ is the regularized incomplete beta function.

    */

    class CumulativeStudentDistribution {

      public:

        CumulativeStudentDistribution(Integer n) : n_(n) {

            QL_REQUIRE(n > 0, "invalid parameter for t-distribution");

        }

        Real operator()(Real x) const;

      private:

        Integer n_;

    };

    //! Inverse cumulative Student t-distribution

    /*! \todo Find/implement an efficient algorithm for evaluating the

              cumulative Student t-distribution, replacing the Newton

              iteration

    */

    class InverseCumulativeStudent {

      public:

        InverseCumulativeStudent(Integer n,

                                 Real accuracy = 1e-6,

                                 Size maxIterations = 50)

        : d_(n), f_(n), accuracy_(accuracy),

          maxIterations_(maxIterations) {}

        Real operator()(Real x) const;

      private:

        StudentDistribution d_;

        CumulativeStudentDistribution f_;

        Real accuracy_;

        Size maxIterations_;

    };

}

#endif