1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LOG_HPP
19 #include <boost/random/variate_generator.hpp>
27 template <
bool propto,
28 typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
29 typename return_type<T_y, T_loc, T_scale, T_shape>::type
31 const T_shape& alpha) {
32 static const char*
function(
"stan::math::pareto_type_2_log");
55 T_partials_return logp(0.0);
64 "Scale parameter", lambda,
65 "Shape parameter", alpha);
76 size_t N =
max_size(y, mu, lambda, alpha);
80 operands_and_partials(y, mu, lambda, alpha);
84 T_partials_return, T_y, T_loc, T_scale>
87 for (
size_t n = 0; n < N; n++)
94 T_partials_return, T_scale> log_lambda(
length(lambda));
96 for (
size_t n = 0; n <
length(lambda); n++)
101 T_partials_return, T_shape> log_alpha(
length(alpha));
103 for (
size_t n = 0; n <
length(alpha); n++)
108 T_partials_return, T_shape> inv_alpha(
length(alpha));
110 for (
size_t n = 0; n <
length(alpha); n++)
111 inv_alpha[n] = 1 /
value_of(alpha_vec[n]);
114 for (
size_t n = 0; n < N; n++) {
115 const T_partials_return y_dbl =
value_of(y_vec[n]);
116 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
117 const T_partials_return lambda_dbl =
value_of(lambda_vec[n]);
118 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
119 const T_partials_return sum_dbl = lambda_dbl + y_dbl - mu_dbl;
120 const T_partials_return inv_sum = 1.0 / sum_dbl;
121 const T_partials_return alpha_div_sum = alpha_dbl / sum_dbl;
122 const T_partials_return deriv_1_2 = inv_sum + alpha_div_sum;
126 logp += log_alpha[n];
128 logp -= log_lambda[n];
130 logp -= (alpha_dbl + 1.0) * log1p_scaled_diff[n];
134 operands_and_partials.
d_x1[n] -= deriv_1_2;
136 operands_and_partials.
d_x2[n] += deriv_1_2;
138 operands_and_partials.
d_x3[n] -= alpha_div_sum * (mu_dbl - y_dbl)
139 / lambda_dbl + inv_sum;
141 operands_and_partials.
d_x4[n] += inv_alpha[n] - log1p_scaled_diff[n];
143 return operands_and_partials.
value(logp);
146 template <
typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
150 const T_scale& lambda,
const T_shape& alpha) {
151 return pareto_type_2_log<false>(y, mu, lambda, alpha);
VectorView< T_return_type, false, true > d_x2
bool check_greater_or_equal(const char *function, const char *name, const T_y &y, const T_low &low)
Return true if y is greater or equal than low.
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
fvar< T > log(const fvar< T > &x)
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
size_t length(const std::vector< T > &x)
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
This class builds partial derivatives with respect to a set of operands.
VectorView< T_return_type, false, true > d_x3
size_t max_size(const T1 &x1, const T2 &x2)
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
VectorBuilder allocates type T1 values to be used as intermediate values.
bool check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Return true if the dimension of x1 is consistent with x2.
fvar< T > log1p(const fvar< T > &x)
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
VectorView is a template expression that is constructed with a container or scalar, which it then allows to be used as an array using operator[].
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
VectorView< T_return_type, false, true > d_x1
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_log(const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
VectorView< T_return_type, false, true > d_x4