1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CDF_HPP 16 #include <boost/random/normal_distribution.hpp> 17 #include <boost/random/variate_generator.hpp> 23 template <
typename T_y,
typename T_loc,
typename T_scale,
27 const T_inv_scale& lambda) {
28 static const char*
function(
"exp_mod_normal_cdf");
33 T_partials_return cdf(1.0);
48 "Location parameter", mu,
49 "Scale parameter", sigma,
50 "Inv_scale paramter", lambda);
53 operands_and_partials(y, mu, sigma, lambda);
61 size_t N =
max_size(y, mu, sigma, lambda);
63 for (
size_t n = 0; n < N; n++) {
66 return operands_and_partials.
value(0.0);
69 const T_partials_return y_dbl =
value_of(y_vec[n]);
70 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
71 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
72 const T_partials_return lambda_dbl =
value_of(lambda_vec[n]);
73 const T_partials_return u = lambda_dbl * (y_dbl - mu_dbl);
74 const T_partials_return v = lambda_dbl * sigma_dbl;
75 const T_partials_return v_sq = v * v;
76 const T_partials_return scaled_diff = (y_dbl - mu_dbl) / (
SQRT_2 78 const T_partials_return scaled_diff_sq = scaled_diff * scaled_diff;
79 const T_partials_return erf_calc = 0.5 * (1 +
erf(-v /
SQRT_2 81 const T_partials_return deriv_1 = lambda_dbl *
exp(0.5 * v_sq - u)
83 const T_partials_return deriv_2 =
SQRT_2 / sqrt_pi * 0.5
84 *
exp(0.5 * v_sq - (scaled_diff - (v /
SQRT_2))
85 * (scaled_diff - (v /
SQRT_2)) - u) / sigma_dbl;
86 const T_partials_return deriv_3 =
SQRT_2 / sqrt_pi * 0.5
87 *
exp(-scaled_diff_sq) / sigma_dbl;
89 const T_partials_return cdf_ = 0.5 * (1 +
erf(u / (v *
SQRT_2)))
90 -
exp(-u + v_sq * 0.5) * (erf_calc);
95 operands_and_partials.
d_x1[n] += (deriv_1 - deriv_2 + deriv_3)
98 operands_and_partials.
d_x2[n] += (-deriv_1 + deriv_2 - deriv_3)
101 operands_and_partials.
d_x3[n] += (-deriv_1 * v - deriv_3
102 * scaled_diff * SQRT_2 - deriv_2
105 * (-lambda_dbl + scaled_diff
106 * SQRT_2 / sigma_dbl) - SQRT_2
107 * lambda_dbl)) / cdf_;
109 operands_and_partials.
d_x4[n] +=
exp(0.5 * v_sq - u)
110 * (SQRT_2 / sqrt_pi * 0.5 * sigma_dbl
111 *
exp(-(v / SQRT_2 - scaled_diff) * (v / SQRT_2 - scaled_diff))
112 - (v * sigma_dbl + mu_dbl - y_dbl) * erf_calc) / cdf_;
117 operands_and_partials.
d_x1[n] *= cdf;
121 operands_and_partials.
d_x2[n] *= cdf;
125 operands_and_partials.
d_x3[n] *= cdf;
129 operands_and_partials.
d_x4[n] *= cdf;
131 return operands_and_partials.
value(cdf);
VectorView< T_return_type, false, true > d_x2
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
fvar< T > sqrt(const fvar< T > &x)
T value_of(const fvar< T > &v)
Return the value of the specified variable.
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
size_t length(const std::vector< T > &x)
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
fvar< T > erf(const fvar< T > &x)
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
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
const double SQRT_2
The value of the square root of 2, .
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
fvar< T > exp(const fvar< T > &x)
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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)
int is_inf(const fvar< T > &x)
Returns 1 if the input's value is infinite and 0 otherwise.
double pi()
Return the value of pi.
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
VectorView< T_return_type, false, true > d_x1
VectorView< T_return_type, false, true > d_x4