1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_CDF_LOG_HPP
18 #include <boost/random/variate_generator.hpp>
25 template <
typename T_y,
typename T_loc,
typename T_scale,
typename T_shape>
26 typename return_type<T_y, T_loc, T_scale, T_shape>::type
28 const T_scale& lambda,
const T_shape& alpha) {
42 static const char*
function(
"stan::math::pareto_type_2_cdf_log");
55 T_partials_return P(0.0);
64 "Scale parameter", lambda,
65 "Shape parameter", alpha);
72 size_t N =
max_size(y, mu, lambda, alpha);
75 operands_and_partials(y, mu, lambda, alpha);
78 T_y, T_loc, T_scale, T_shape>
82 T_y, T_loc, T_scale, T_shape>
83 inv_p1_pow_alpha_minus_one(N);
86 T_partials_return, T_y, T_loc, T_scale, T_shape>
87 log_1p_y_over_lambda(N);
89 for (
size_t i = 0; i < N; i++) {
90 const T_partials_return temp = 1.0 + (
value_of(y_vec[i])
93 const T_partials_return p1_pow_alpha
95 cdf_log[i] =
log1m(1.0 / p1_pow_alpha);
97 inv_p1_pow_alpha_minus_one[i] = 1.0 / (p1_pow_alpha - 1.0);
100 log_1p_y_over_lambda[i] =
log(temp);
105 for (
size_t n = 0; n < N; n++) {
107 const T_partials_return y_dbl =
value_of(y_vec[n]);
108 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
109 const T_partials_return lambda_dbl =
value_of(lambda_vec[n]);
110 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
112 const T_partials_return grad_1_2 = alpha_dbl
113 * inv_p1_pow_alpha_minus_one[n] / (lambda_dbl - mu_dbl + y_dbl);
119 operands_and_partials.
d_x1[n] += grad_1_2;
121 operands_and_partials.
d_x2[n] -= grad_1_2;
123 operands_and_partials.
d_x3[n] += (mu_dbl - y_dbl) * grad_1_2
126 operands_and_partials.
d_x4[n] += log_1p_y_over_lambda[n]
127 * inv_p1_pow_alpha_minus_one[n];
130 return operands_and_partials.
value(P);
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)
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.
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_cdf_log(const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
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 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.
fvar< T > log1m(const fvar< T > &x)
VectorView< T_return_type, false, true > d_x1
VectorView< T_return_type, false, true > d_x4