1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_CDF_HPP
4 #include <boost/random/variate_generator.hpp>
23 template <
typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
24 typename return_type<T_y, T_loc, T_scale, T_shape>::type
26 const T_scale& lambda,
const T_shape& alpha) {
40 static const char*
function(
"stan::math::pareto_type_2_cdf");
52 T_partials_return P(1.0);
61 "Scale parameter", lambda,
62 "Shape parameter", alpha);
69 size_t N =
max_size(y, mu, lambda, alpha);
72 operands_and_partials(y, mu, lambda, alpha);
75 T_y, T_loc, T_scale, T_shape>
79 T_partials_return, T_y, T_loc, T_scale, T_shape>
83 T_partials_return, T_y, T_loc, T_scale, T_shape>
86 for (
size_t i = 0; i < N; i++) {
87 const T_partials_return lambda_dbl =
value_of(lambda_vec[i]);
88 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
89 const T_partials_return temp = 1 + (
value_of(y_vec[i])
92 p1_pow_alpha[i] =
pow(temp, -alpha_dbl);
95 grad_1_2[i] = p1_pow_alpha[i] / temp * alpha_dbl / lambda_dbl;
98 grad_3[i] =
log(temp) * p1_pow_alpha[i];
103 for (
size_t n = 0; n < N; n++) {
105 const T_partials_return y_dbl =
value_of(y_vec[n]);
106 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
107 const T_partials_return lambda_dbl =
value_of(lambda_vec[n]);
109 const T_partials_return Pn = 1.0 - p1_pow_alpha[n];
115 operands_and_partials.
d_x1[n] += grad_1_2[n] / Pn;
117 operands_and_partials.
d_x2[n] -= grad_1_2[n] / Pn;
119 operands_and_partials.
d_x3[n] += (mu_dbl - y_dbl)
120 * grad_1_2[n] / lambda_dbl / Pn;
122 operands_and_partials.
d_x4[n] += grad_3[n] / Pn;
127 operands_and_partials.
d_x1[n] *= P;
131 operands_and_partials.
d_x2[n] *= P;
135 operands_and_partials.
d_x3[n] *= P;
139 operands_and_partials.
d_x4[n] *= P;
142 return operands_and_partials.
to_var(P, 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)
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_cdf(const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
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)
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 > pow(const fvar< T > &x1, const fvar< T > &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 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.