weibull.hpp

Go to the documentation of this file.

/** \file weibull.hpp
 * \brief The Weibull distribution.
 * \ingroup gen_math_files
 * \author Jared R. Males (jaredmales@gmail.com)
 *
 */
 
//***********************************************************************//
// Copyright 2015, 2016, 2017 Jared R. Males (jaredmales@gmail.com)
//
// This file is part of mxlib.
//
// mxlib is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// mxlib 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 General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with mxlib.  If not, see <http://www.gnu.org/licenses/>.
//***********************************************************************//
 
#ifndef weibull_hpp
#define weibull_hpp
 
namespace mx
{
namespace math
{
namespace func
{
 
/// The MLE of the Weibull distribution lambda parameter.
/**
 * \tparam realT a real floating point type
 *
 * \returns the MLE of lambda given the data.
 *
 * \ingroup gen_math_weibull
 */
template <typename realT>
realT weibull_lambda( std::vector<realT> &x, ///<[in] the data points
                      realT k,               ///< [in] the shape parameter
                      realT x0 = 0           ///< [in] [optional] the location parameter
)
{
    int n = x.size();
 
    realT lambda = 0;
 
    for( int i = 0; i < n; ++i )
        lambda += pow( x[i] - x0, k );
 
    lambda /= n;
 
    return pow( lambda, 1.0 / k );
}
 
/// The general shifted Weibull distribution at a point.
/** Calculates the value of the Weibull distribution at a location specified by x.
 *
 * \f[
 *
 * f(x; x_o, \lambda, k) =
 * \begin{cases}
 * \frac{k}{\lambda}\left( \frac{x-x_o}{\lambda}\right)^{k-1} \exp \left( -\left(\frac{x-x_o}{\lambda}\right)^k \right),
 * & x \ge 0 \\ 0, & x < 0 \end{cases} \f]
 *
 * \tparam realT a real floating point type
 *
 * \returns the value of the Weibull distribution at x.
 *
 * \ingroup gen_math_weibull
 */
template <typename realT>
realT weibull( realT x,     ///< [in] the location at which to calculate the distribution
               realT x0,    ///< [in] the location parameter
               realT k,     ///< [in] the shape parameter
               realT lambda ///< [in] the scale parameter
)
{
    if( x - x0 < 0 )
        return 0.0;
 
    realT rat = ( x - x0 ) / lambda;
 
    return ( k / lambda ) * pow( rat, k - 1 ) * exp( -pow( rat, k ) );
}
 
/// The Weibull distribution at a point.
/** Calculates the value of the Weibull distribution at a location specified by x.
 *
 * \f[
 *
 * f(x; \lambda, k) =
 * \begin{cases}
 * \frac{k}{\lambda}\left( \frac{x}{\lambda}\right)^{k-1} \exp \left( -\left(\frac{x}{\lambda}\right)^k \right), & x \ge
 * 0 \\ 0, & x < 0 \end{cases} \f]
 *
 * \tparam realT a real floating point type
 *
 * \returns the value of the Weibull distribution at x.
 *
 * \overload
 *
 * \ingroup gen_math_weibull
 */
template <typename realT>
realT weibull( realT x,     ///< [in] the location at which to calculate the distribution
               realT k,     ///< [in] the shape parameter
               realT lambda ///< [in] the scale parameter
)
{
    return weibull( x, static_cast<realT>( 0 ), k, lambda );
}
 
} // namespace func
} // namespace math
} // namespace mx
 
#endif // weibull_hpp