// Arguments: Doubles, Doubles, Doubles, Doubles
#include <stan/math/prim/prob/pareto_type_2_lpdf.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <stan/math/prim/fun/log1p.hpp>

using stan::math::var;
using std::numeric_limits;
using std::vector;

class AgradDistributionParetoType2 : public AgradDistributionTest {
 public:
  void valid_values(vector<vector<double> >& parameters,
                    vector<double>& log_prob) {
    vector<double> param(4);

    param[0] = 1.5;  // y
    param[1] = 0.1;  // mu
    param[2] = 0.5;  // lambda
    param[3] = 3.0;  // alpha
    parameters.push_back(param);
    log_prob.push_back(-3.548244797701304964476776149240);  // expected log_prob

    param[0] = 19.5;  // y
    param[1] = 0;     // mu
    param[2] = 0.15;  // lambda
    param[3] = 5.0;   // alpha
    parameters.push_back(param);
    log_prob.push_back(-25.74462604188692758825580639457);  // expected log_prob
  }

  void invalid_values(vector<size_t>& index, vector<double>& value) {
    // y
    index.push_back(0U);
    value.push_back(-1.0);

    // lambda
    index.push_back(2U);
    value.push_back(0.0);

    index.push_back(2U);
    value.push_back(-1.0);

    index.push_back(2U);
    value.push_back(numeric_limits<double>::infinity());

    index.push_back(2U);
    value.push_back(-numeric_limits<double>::infinity());

    // alpha
    index.push_back(3U);
    value.push_back(0.0);

    index.push_back(3U);
    value.push_back(-1.0);

    index.push_back(3U);
    value.push_back(numeric_limits<double>::infinity());

    index.push_back(3U);
    value.push_back(-numeric_limits<double>::infinity());
  }

  template <class T_y, class T_loc, class T_scale, class T_shape, typename T4,
            typename T5>
  stan::return_type_t<T_y, T_scale, T_shape, T_loc> log_prob(
      const T_y& y, const T_loc& mu, const T_scale& lambda,
      const T_shape& alpha, const T4&, const T5&) {
    return stan::math::pareto_type_2_lpdf(y, mu, lambda, alpha);
  }

  template <bool propto, class T_y, class T_loc, class T_scale, class T_shape,
            typename T4, typename T5>
  stan::return_type_t<T_y, T_loc, T_scale, T_shape> log_prob(
      const T_y& y, const T_loc& mu, const T_scale& lambda,
      const T_shape& alpha, const T4&, const T5&) {
    return stan::math::pareto_type_2_lpdf<propto>(y, mu, lambda, alpha);
  }

  template <class T_y, class T_loc, class T_scale, class T_shape, typename T4,
            typename T5>
  stan::return_type_t<T_y, T_loc, T_scale, T_shape> log_prob_function(
      const T_y& y, const T_loc& mu, const T_scale& lambda,
      const T_shape& alpha, const T4&, const T5&) {
    return log(alpha) - log(lambda) - (alpha + 1.0) * log1p((y - mu) / lambda);
  }
};
