1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_CCDF_LOG_HPP
14 #include <boost/random/normal_distribution.hpp>
15 #include <boost/math/special_functions/fpclassify.hpp>
16 #include <boost/random/variate_generator.hpp>
23 template <
typename T_y,
typename T_loc,
typename T_scale,
25 typename return_type<T_y, T_loc, T_scale, T_inv_scale>::type
27 const T_inv_scale& lambda) {
28 static const char*
function(
"stan::math::exp_mod_normal_ccdf_log");
39 T_partials_return ccdf_log(0.0);
55 "Location parameter", mu,
56 "Scale parameter", sigma,
57 "Inv_scale paramter", lambda);
61 operands_and_partials(y, mu, sigma, lambda);
72 size_t N =
max_size(y, mu, sigma, lambda);
74 for (
size_t n = 0; n < N; n++) {
79 return operands_and_partials.
value(0.0);
82 const T_partials_return y_dbl =
value_of(y_vec[n]);
83 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
84 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
85 const T_partials_return lambda_dbl =
value_of(lambda_vec[n]);
86 const T_partials_return u = lambda_dbl * (y_dbl - mu_dbl);
87 const T_partials_return v = lambda_dbl * sigma_dbl;
88 const T_partials_return v_sq = v * v;
89 const T_partials_return scaled_diff = (y_dbl - mu_dbl)
91 const T_partials_return scaled_diff_sq = scaled_diff * scaled_diff;
92 const T_partials_return erf_calc1 = 0.5 * (1 +
erf(u / (v *
SQRT_2)));
93 const T_partials_return erf_calc2 = 0.5 * (1 +
erf(u / (v * SQRT_2)
96 const T_partials_return deriv_1 = lambda_dbl *
exp(0.5 * v_sq - u)
98 const T_partials_return deriv_2 = SQRT_2 / sqrt_pi * 0.5
100 - (-scaled_diff + (v / SQRT_2)) * (-scaled_diff
103 const T_partials_return deriv_3 = SQRT_2 / sqrt_pi * 0.5
104 *
exp(-scaled_diff_sq) / sigma_dbl;
106 const T_partials_return ccdf_ = 1.0 - erf_calc1 +
exp(-u + v_sq * 0.5)
109 ccdf_log +=
log(ccdf_);
112 operands_and_partials.
d_x1[n]
113 -= (deriv_1 - deriv_2 + deriv_3) / ccdf_;
115 operands_and_partials.
d_x2[n]
116 -= (-deriv_1 + deriv_2 - deriv_3) / ccdf_;
118 operands_and_partials.
d_x3[n]
119 -= (-deriv_1 * v - deriv_3 * scaled_diff * SQRT_2 - deriv_2
121 * (-SQRT_2 * 0.5 * (-lambda_dbl + scaled_diff * SQRT_2
123 - SQRT_2 * lambda_dbl))
126 operands_and_partials.
d_x4[n] -=
exp(0.5 * v_sq - u)
127 * (SQRT_2 / sqrt_pi * 0.5 * sigma_dbl
128 *
exp(-(v / SQRT_2 - scaled_diff) * (v / SQRT_2 - scaled_diff))
129 - (v * sigma_dbl + mu_dbl - y_dbl) * erf_calc2)
133 return operands_and_partials.
value(ccdf_log);
VectorView< T_return_type, false, true > d_x2
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.
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)
fvar< T > erf(const fvar< T > &x)
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)
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.
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.
double pi()
Return the value of pi.
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[].
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_ccdf_log(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
VectorView< T_return_type, false, true > d_x1
double negative_infinity()
Return negative infinity.
VectorView< T_return_type, false, true > d_x4