1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LCDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LCDF_HPP 15 #include <boost/random/normal_distribution.hpp> 16 #include <boost/random/variate_generator.hpp> 22 template <
typename T_y,
typename T_loc,
typename T_scale,
26 const T_inv_scale& lambda) {
27 static const char*
function(
"exp_mod_normal_lcdf");
32 T_partials_return cdf_log(0.0);
47 "Location parameter", mu,
48 "Scale parameter", sigma,
49 "Inv_scale paramter", lambda);
52 operands_and_partials(y, mu, sigma, lambda);
62 size_t N =
max_size(y, mu, sigma, lambda);
64 for (
size_t n = 0; n < N; n++) {
69 return operands_and_partials.
value(0.0);
72 const T_partials_return y_dbl =
value_of(y_vec[n]);
73 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
74 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
75 const T_partials_return lambda_dbl =
value_of(lambda_vec[n]);
76 const T_partials_return u = lambda_dbl * (y_dbl - mu_dbl);
77 const T_partials_return v = lambda_dbl * sigma_dbl;
78 const T_partials_return v_sq = v * v;
79 const T_partials_return scaled_diff = (y_dbl - mu_dbl)
81 const T_partials_return scaled_diff_sq = scaled_diff * scaled_diff;
82 const T_partials_return erf_calc1 = 0.5 * (1 +
erf(u / (v *
SQRT_2)));
83 const T_partials_return erf_calc2 = 0.5 * (1 +
erf(u / (v * SQRT_2) - v
85 const T_partials_return deriv_1 = lambda_dbl *
exp(0.5 * v_sq - u)
87 const T_partials_return deriv_2 = SQRT_2 / sqrt_pi * 0.5
88 *
exp(0.5 * v_sq - (-scaled_diff + (v / SQRT_2))
89 * (-scaled_diff + (v / SQRT_2)) - u) / sigma_dbl;
90 const T_partials_return deriv_3 = SQRT_2 / sqrt_pi * 0.5
91 *
exp(-scaled_diff_sq) / sigma_dbl;
93 const T_partials_return denom = erf_calc1 - erf_calc2
94 *
exp(0.5 * v_sq - u);
95 const T_partials_return cdf_ = erf_calc1 -
exp(-u + v_sq * 0.5)
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]
108 += (-deriv_1 * v - deriv_3 * scaled_diff
109 * SQRT_2 - deriv_2 * sigma_dbl * SQRT_2
110 * (-SQRT_2 * 0.5 * (-lambda_dbl + scaled_diff * SQRT_2
112 - SQRT_2 * lambda_dbl))
115 operands_and_partials.
d_x4[n]
116 +=
exp(0.5 * v_sq - u)
117 * (SQRT_2 / sqrt_pi * 0.5 * sigma_dbl
118 *
exp(-(v / SQRT_2 - scaled_diff)
119 * (v / SQRT_2 - scaled_diff))
120 - (v * sigma_dbl + mu_dbl - y_dbl) * erf_calc2)
123 return operands_and_partials.
value(cdf_log);
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.
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)
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
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_lcdf(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
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.
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[].
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
double negative_infinity()
Return negative infinity.
VectorView< T_return_type, false, true > d_x4