student_t.hpp

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#ifndef __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__CONTINUOUS__STUDENT_T_HPP__
#define __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__CONTINUOUS__STUDENT_T_HPP__

#include <stan/agrad.hpp>
#include <stan/math/error_handling.hpp>
#include <stan/math/special_functions.hpp>
#include <stan/meta/traits.hpp>
#include <stan/prob/constants.hpp>
#include <stan/prob/traits.hpp>

namespace stan {

  namespace prob {

    template <bool propto, typename T_y, typename T_dof, 
              typename T_loc, typename T_scale,
              class Policy>
    typename return_type<T_y,T_dof,T_loc,T_scale>::type
    student_t_log(const T_y& y, const T_dof& nu, const T_loc& mu, 
                  const T_scale& sigma, 
                  const Policy&) {
      static const char* function = "stan::prob::student_t_log(%1%)";

      using stan::math::check_positive;
      using stan::math::check_finite;
      using stan::math::check_not_nan;
      using stan::math::check_consistent_sizes;

      // check if any vectors are zero length
      if (!(stan::length(y) 
            && stan::length(nu) 
            && stan::length(mu)
            && stan::length(sigma)))
        return 0.0;

      typename return_type<T_y,T_dof,T_loc,T_scale>::type logp = 0.0;

      // validate args (here done over var, which should be OK)
      if (!check_not_nan(function, y, "Random variable", &logp, Policy()))
        return logp;
      if(!check_finite(function, nu, "Degrees of freedom parameter", &logp, Policy()))
        return logp;
      if(!check_positive(function, nu, "Degrees of freedom parameter", &logp, Policy()))
        return logp;
      if (!check_finite(function, mu, "Location parameter", 
                        &logp, Policy()))
        return logp;
      if (!check_finite(function, sigma, "Scale parameter", 
                        &logp, Policy()))
        return logp;
      if (!check_positive(function, sigma, "Scale parameter", 
                          &logp, Policy()))
        return logp;

      
      if (!(check_consistent_sizes(function,
                                   y,nu,mu,sigma,
                                   "Random variable","Degrees of freedom parameter","Location parameter","Scale parameter",
                                   &logp, Policy())))
        return logp;

      // check if no variables are involved and prop-to
      if (!include_summand<propto,T_y,T_dof,T_loc,T_scale>::value)
        return 0.0;

      VectorView<const T_y> y_vec(y);
      VectorView<const T_dof> nu_vec(nu);
      VectorView<const T_loc> mu_vec(mu);
      VectorView<const T_scale> sigma_vec(sigma);
      size_t N = max_size(y, nu, mu, sigma);

      using stan::math::square;
      using boost::math::lgamma;

      using std::log;

      for (size_t n = 0; n < N; n++) {
        if (include_summand<propto,T_dof>::value)
          logp += lgamma( (nu_vec[n] + 1.0) / 2.0) - lgamma(nu_vec[n] / 2.0);
        if (include_summand<propto>::value)
          logp += NEG_LOG_SQRT_PI;
        if (include_summand<propto,T_dof>::value)
          logp -= 0.5 * log(nu_vec[n]);
        if (include_summand<propto,T_scale>::value)
          logp -= log(sigma_vec[n]);
        if (include_summand<propto,T_y,T_dof,T_loc,T_scale>::value)
          logp -= ((nu_vec[n] + 1.0) / 2.0) 
            * log1p( square(((y_vec[n] - mu_vec[n]) / sigma_vec[n])) / nu_vec[n]);
      }
      return logp;
    }

    template <bool propto, 
              typename T_y, typename T_dof, typename T_loc, typename T_scale>
    inline
    typename return_type<T_y,T_dof,T_loc,T_scale>::type
    student_t_log(const T_y& y, const T_dof& nu, const T_loc& mu, 
                  const T_scale& sigma) {
      return student_t_log<propto>(y,nu,mu,sigma,stan::math::default_policy());
    }

    template <typename T_y, typename T_dof, typename T_loc, typename T_scale,
              class Policy>
    inline
    typename return_type<T_y,T_dof,T_loc,T_scale>::type
    student_t_log(const T_y& y, const T_dof& nu, const T_loc& mu, 
                  const T_scale& sigma, 
                  const Policy&) {
      return student_t_log<false>(y,nu,mu,sigma,Policy());
    }

    template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
    inline
    typename return_type<T_y,T_dof,T_loc,T_scale>::type
    student_t_log(const T_y& y, const T_dof& nu, const T_loc& mu, 
                  const T_scale& sigma) {
      return student_t_log<false>(y,nu,mu,sigma,stan::math::default_policy());
    }

    
  }
}
#endif