1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CDF_HPP
4 #include <boost/random/cauchy_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
34 template <
typename T_y,
typename T_loc,
typename T_scale>
35 typename return_type<T_y, T_loc, T_scale>::type
36 cauchy_cdf(
const T_y& y,
const T_loc& mu,
const T_scale& sigma) {
45 static const char*
function(
"stan::math::cauchy_cdf");
51 using boost::math::tools::promote_args;
54 T_partials_return P(1.0);
61 "Location parameter", mu,
62 "Scale Parameter", sigma);
71 operands_and_partials(y, mu, sigma);
76 if (
value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
77 return operands_and_partials.
to_var(0.0, y, mu, sigma);
85 for (
size_t n = 0; n < N; n++) {
88 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
93 const T_partials_return y_dbl =
value_of(y_vec[n]);
94 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
95 const T_partials_return sigma_inv_dbl = 1.0 /
value_of(sigma_vec[n]);
97 const T_partials_return z = (y_dbl - mu_dbl) * sigma_inv_dbl;
100 const T_partials_return Pn =
atan(z) /
pi() + 0.5;
105 operands_and_partials.
d_x1[n]
106 += sigma_inv_dbl / (
pi() * (1.0 + z * z) * Pn);
108 operands_and_partials.
d_x2[n]
109 += - sigma_inv_dbl / (
pi() * (1.0 + z * z) * Pn);
111 operands_and_partials.
d_x3[n]
112 += - z * sigma_inv_dbl / (
pi() * (1.0 + z * z) * Pn);
117 operands_and_partials.
d_x1[n] *= P;
121 operands_and_partials.
d_x2[n] *= P;
125 operands_and_partials.
d_x3[n] *= P;
128 return operands_and_partials.
to_var(P, y, mu, sigma);
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.
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)
fvar< T > atan(const fvar< T > &x)
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
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.
return_type< T_y, T_loc, T_scale >::type cauchy_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
Calculates the cauchy cumulative distribution function for the given variate, location, and scale.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
double pi()
Return the value of pi.
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.