1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_CDF_HPP
15 #include <boost/random/exponential_distribution.hpp>
16 #include <boost/random/variate_generator.hpp>
23 template <
typename T_y,
typename T_scale,
typename T_shape>
24 typename return_type<T_y, T_scale, T_shape>::type
25 pareto_cdf(
const T_y& y,
const T_scale& y_min,
const T_shape& alpha) {
32 static const char*
function(
"pareto_cdf");
37 T_partials_return P(1.0);
45 "Scale parameter", y_min,
46 "Shape parameter", alpha);
51 size_t N =
max_size(y, y_min, alpha);
54 operands_and_partials(y, y_min, alpha);
60 return operands_and_partials.
value(0.0);
64 for (
size_t n = 0; n < N; n++) {
67 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
71 const T_partials_return log_dbl =
log(
value_of(y_min_vec[n])
73 const T_partials_return y_min_inv_dbl = 1.0 /
value_of(y_min_vec[n]);
74 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
76 const T_partials_return Pn = 1.0 -
exp(alpha_dbl * log_dbl);
81 operands_and_partials.
d_x1[n]
82 += alpha_dbl * y_min_inv_dbl *
exp((alpha_dbl + 1) * log_dbl)
85 operands_and_partials.
d_x2[n]
86 += - alpha_dbl * y_min_inv_dbl *
exp(alpha_dbl * log_dbl) / Pn;
88 operands_and_partials.
d_x3[n]
89 += -
exp(alpha_dbl * log_dbl) * log_dbl / Pn;
94 operands_and_partials.
d_x1[n] *= P;
98 operands_and_partials.
d_x2[n] *= P;
102 operands_and_partials.
d_x3[n] *= P;
104 return operands_and_partials.
value(P);
VectorView< T_return_type, false, true > d_x2
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)
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
fvar< T > exp(const fvar< T > &x)
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)
return_type< T_y, T_scale, T_shape >::type pareto_cdf(const T_y &y, const T_scale &y_min, const T_shape &alpha)
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.
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