1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CDF_HPP
4 #include <boost/random/normal_distribution.hpp>
5 #include <boost/math/special_functions/fpclassify.hpp>
6 #include <boost/random/variate_generator.hpp>
21 template <
typename T_y,
typename T_loc,
typename T_scale,
23 typename return_type<T_y, T_loc, T_scale, T_inv_scale>::type
25 const T_inv_scale& lambda) {
26 static const char*
function(
"stan::math::exp_mod_normal_cdf");
37 T_partials_return cdf(1.0);
53 "Location parameter", mu,
54 "Scale parameter", sigma,
55 "Inv_scale paramter", lambda);
58 operands_and_partials(y, mu, sigma, lambda);
67 size_t N =
max_size(y, mu, sigma, lambda);
69 for (
size_t n = 0; n < N; n++) {
72 return operands_and_partials.
to_var(0.0, y, mu, sigma, lambda);
75 const T_partials_return y_dbl =
value_of(y_vec[n]);
76 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
77 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
78 const T_partials_return lambda_dbl =
value_of(lambda_vec[n]);
79 const T_partials_return u = lambda_dbl * (y_dbl - mu_dbl);
80 const T_partials_return v = lambda_dbl * sigma_dbl;
81 const T_partials_return v_sq = v * v;
82 const T_partials_return scaled_diff = (y_dbl - mu_dbl) / (
SQRT_2
84 const T_partials_return scaled_diff_sq = scaled_diff * scaled_diff;
85 const T_partials_return erf_calc = 0.5 * (1 +
erf(-v /
SQRT_2
87 const T_partials_return deriv_1 = lambda_dbl *
exp(0.5 * v_sq - u)
89 const T_partials_return deriv_2 =
SQRT_2 / sqrt_pi * 0.5
90 *
exp(0.5 * v_sq - (scaled_diff - (v /
SQRT_2))
91 * (scaled_diff - (v /
SQRT_2)) - u) / sigma_dbl;
92 const T_partials_return deriv_3 =
SQRT_2 / sqrt_pi * 0.5
93 *
exp(-scaled_diff_sq) / sigma_dbl;
95 const T_partials_return cdf_ = 0.5 * (1 +
erf(u / (v *
SQRT_2)))
96 -
exp(-u + v_sq * 0.5) * (erf_calc);
101 operands_and_partials.
d_x1[n] += (deriv_1 - deriv_2 + deriv_3)
104 operands_and_partials.
d_x2[n] += (-deriv_1 + deriv_2 - deriv_3)
107 operands_and_partials.
d_x3[n] += (-deriv_1 * v - deriv_3
108 * scaled_diff * SQRT_2 - deriv_2
111 * (-lambda_dbl + scaled_diff
112 * SQRT_2 / sigma_dbl) - SQRT_2
113 * lambda_dbl)) / cdf_;
115 operands_and_partials.
d_x4[n] +=
exp(0.5 * v_sq - u)
116 * (SQRT_2 / sqrt_pi * 0.5 * sigma_dbl
117 *
exp(-(v / SQRT_2 - scaled_diff) * (v / SQRT_2 - scaled_diff))
118 - (v * sigma_dbl + mu_dbl - y_dbl) * erf_calc) / cdf_;
123 operands_and_partials.
d_x1[n] *= cdf;
127 operands_and_partials.
d_x2[n] *= cdf;
131 operands_and_partials.
d_x3[n] *= cdf;
135 operands_and_partials.
d_x4[n] *= cdf;
138 return operands_and_partials.
to_var(cdf, y, mu, sigma, lambda);
fvar< T > sqrt(const fvar< T > &x)
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)
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)
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...
const double SQRT_2
The value of the square root of 2, .
bool isinf(const stan::math::var &v)
Checks if the given number is infinite.
fvar< T > exp(const fvar< T > &x)
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
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...
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.