1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LOG_HPP
4 #include <boost/random/variate_generator.hpp>
25 template <
bool propto,
26 typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
27 typename return_type<T_y, T_loc, T_scale, T_shape>::type
29 const T_shape& alpha) {
30 static const char*
function(
"stan::math::pareto_type_2_log");
53 T_partials_return logp(0.0);
62 "Scale parameter", lambda,
63 "Shape parameter", alpha);
74 size_t N =
max_size(y, mu, lambda, alpha);
78 operands_and_partials(y, mu, lambda, alpha);
82 T_partials_return, T_y, T_loc, T_scale>
85 for (
size_t n = 0; n < N; n++)
92 T_partials_return, T_scale> log_lambda(
length(lambda));
94 for (
size_t n = 0; n <
length(lambda); n++)
99 T_partials_return, T_shape> log_alpha(
length(alpha));
101 for (
size_t n = 0; n <
length(alpha); n++)
106 T_partials_return, T_shape> inv_alpha(
length(alpha));
108 for (
size_t n = 0; n <
length(alpha); n++)
109 inv_alpha[n] = 1 /
value_of(alpha_vec[n]);
112 for (
size_t n = 0; n < N; n++) {
113 const T_partials_return y_dbl =
value_of(y_vec[n]);
114 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
115 const T_partials_return lambda_dbl =
value_of(lambda_vec[n]);
116 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
117 const T_partials_return sum_dbl = lambda_dbl + y_dbl - mu_dbl;
118 const T_partials_return inv_sum = 1.0 / sum_dbl;
119 const T_partials_return alpha_div_sum = alpha_dbl / sum_dbl;
120 const T_partials_return deriv_1_2 = inv_sum + alpha_div_sum;
124 logp += log_alpha[n];
126 logp -= log_lambda[n];
128 logp -= (alpha_dbl + 1.0) * log1p_scaled_diff[n];
132 operands_and_partials.
d_x1[n] -= deriv_1_2;
134 operands_and_partials.
d_x2[n] += deriv_1_2;
136 operands_and_partials.
d_x3[n] -= alpha_div_sum * (mu_dbl - y_dbl)
137 / lambda_dbl + inv_sum;
139 operands_and_partials.
d_x4[n] += inv_alpha[n] - log1p_scaled_diff[n];
141 return operands_and_partials.
to_var(logp, y, mu, lambda, alpha);
144 template <
typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
148 const T_scale& lambda,
const T_shape& alpha) {
149 return pareto_type_2_log<false>(y, mu, lambda, alpha);
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)
size_t length(const std::vector< T > &x)
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
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
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
VectorView< T_partials_return, is_vector< T4 >::value, is_constant_struct< T4 >::value > d_x4
A variable implementation that stores operands and derivatives with respect to the variable...
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.
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_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 metaprogram that takes its argument and allows it to be used like a vector...
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.
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)