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skew_normal_cdf.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CDF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CDF_HPP
#include <boost/random/variate_generator.hpp>
#include <boost/math/distributions.hpp>
#include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
#include <stan/math/prim/scal/err/check_finite.hpp>
#include <stan/math/prim/scal/err/check_not_nan.hpp>
#include <stan/math/prim/scal/err/check_positive.hpp>
#include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
#include <stan/math/prim/scal/fun/owens_t.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/meta/is_constant_struct.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/meta/VectorBuilder.hpp>
#include <stan/math/prim/scal/meta/VectorView.hpp>
#include <cmath>
namespace stan {
namespace math {
template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
typename return_type<T_y, T_loc, T_scale, T_shape>::type
skew_normal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma,
const T_shape& alpha) {
static const char* function("stan::math::skew_normal_cdf");
typedef typename stan::partials_return_type<T_y, T_loc, T_scale,
T_shape>::type
T_partials_return;
using stan::math::check_positive;
using stan::math::check_finite;
using stan::math::check_not_nan;
using stan::math::check_consistent_sizes;
using stan::math::owens_t;
using stan::math::value_of;
T_partials_return cdf(1.0);
// check if any vectors are zero length
if (!(stan::length(y)
&& stan::length(mu)
&& stan::length(sigma)
&& stan::length(alpha)))
return cdf;
check_not_nan(function, "Random variable", y);
check_finite(function, "Location parameter", mu);
check_not_nan(function, "Scale parameter", sigma);
check_positive(function, "Scale parameter", sigma);
check_finite(function, "Shape parameter", alpha);
check_not_nan(function, "Shape parameter", alpha);
check_consistent_sizes(function,
"Random variable", y,
"Location parameter", mu,
"Scale parameter", sigma,
"Shape paramter", alpha);
OperandsAndPartials<T_y, T_loc, T_scale, T_shape>
operands_and_partials(y, mu, sigma, alpha);
using stan::math::SQRT_2;
using stan::math::pi;
using std::exp;
VectorView<const T_y> y_vec(y);
VectorView<const T_loc> mu_vec(mu);
VectorView<const T_scale> sigma_vec(sigma);
VectorView<const T_shape> alpha_vec(alpha);
size_t N = max_size(y, mu, sigma, alpha);
const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / stan::math::pi());
for (size_t n = 0; n < N; n++) {
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return mu_dbl = value_of(mu_vec[n]);
const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
const T_partials_return alpha_dbl_sq = alpha_dbl * alpha_dbl;
const T_partials_return diff = (y_dbl - mu_dbl) / sigma_dbl;
const T_partials_return diff_sq = diff * diff;
const T_partials_return scaled_diff = diff / SQRT_2;
const T_partials_return scaled_diff_sq = diff_sq * 0.5;
const T_partials_return cdf_ = 0.5 * erfc(-scaled_diff) - 2
* owens_t(diff, alpha_dbl);
// cdf
cdf *= cdf_;
// gradients
const T_partials_return deriv_erfc = SQRT_TWO_OVER_PI * 0.5
* exp(-scaled_diff_sq)
/ sigma_dbl;
const T_partials_return deriv_owens = erf(alpha_dbl * scaled_diff)
* exp(-scaled_diff_sq) / SQRT_TWO_OVER_PI / (-2.0 * pi()) / sigma_dbl;
const T_partials_return rep_deriv = (-2.0 * deriv_owens + deriv_erfc)
/ cdf_;
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] += rep_deriv;
if (!is_constant_struct<T_loc>::value)
operands_and_partials.d_x2[n] -= rep_deriv;
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x3[n] -= rep_deriv * diff;
if (!is_constant_struct<T_shape>::value)
operands_and_partials.d_x4[n] += -2.0 * exp(-0.5 * diff_sq
* (1.0 + alpha_dbl_sq))
/ ((1 + alpha_dbl_sq) * 2.0 * pi()) / cdf_;
}
if (!is_constant_struct<T_y>::value) {
for (size_t n = 0; n < stan::length(y); ++n)
operands_and_partials.d_x1[n] *= cdf;
}
if (!is_constant_struct<T_loc>::value) {
for (size_t n = 0; n < stan::length(mu); ++n)
operands_and_partials.d_x2[n] *= cdf;
}
if (!is_constant_struct<T_scale>::value) {
for (size_t n = 0; n < stan::length(sigma); ++n)
operands_and_partials.d_x3[n] *= cdf;
}
if (!is_constant_struct<T_shape>::value) {
for (size_t n = 0; n < stan::length(alpha); ++n)
operands_and_partials.d_x4[n] *= cdf;
}
return operands_and_partials.to_var(cdf, y, mu, sigma, alpha);
}
}
}
#endif
check_not_nan.hpp
stan::math::skew_normal_cdf
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
Definition: skew_normal_cdf.hpp:26
stan::math::sqrt
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:15
stan::math::check_not_nan
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
Definition: check_not_nan.hpp:63
check_positive.hpp
stan::math::value_of
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
stan::math::erf
fvar< T > erf(const fvar< T > &x)
Definition: erf.hpp:14
stan::math::OperandsAndPartials::to_var
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)
Definition: OperandsAndPartials.hpp:322
VectorView.hpp
stan::math::owens_t
fvar< T > owens_t(const fvar< T > &x1, const fvar< T > &x2)
Definition: owens_t.hpp:14
include_summand.hpp
stan::math::OperandsAndPartials::d_x1
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Definition: OperandsAndPartials.hpp:253
stan::is_constant_struct
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
Definition: is_constant_struct.hpp:16
stan::math::SQRT_2
const double SQRT_2
The value of the square root of 2, .
Definition: constants.hpp:21
stan::partials_return_type
Definition: partials_return_type.hpp:16
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
stan::math::OperandsAndPartials::d_x3
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
Definition: OperandsAndPartials.hpp:259
stan::math::OperandsAndPartials::d_x4
VectorView< T_partials_return, is_vector< T4 >::value, is_constant_struct< T4 >::value > d_x4
Definition: OperandsAndPartials.hpp:262
stan::math::OperandsAndPartials
A variable implementation that stores operands and derivatives with respect to the variable...
Definition: OperandsAndPartials.hpp:238
stan::math::check_positive
bool check_positive(const char *function, const char *name, const T_y &y)
Return true if y is positive.
Definition: check_positive.hpp:68
OperandsAndPartials.hpp
owens_t.hpp
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
VectorBuilder.hpp
stan::math::check_finite
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
Definition: check_finite.hpp:62
constants.hpp
stan::math::check_consistent_sizes
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.
Definition: check_consistent_sizes.hpp:31
check_finite.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
Definition: OperandsAndPartials.hpp:256
is_constant_struct.hpp
stan::math::erfc
fvar< T > erfc(const fvar< T > &x)
Definition: erfc.hpp:14
stan::math::pi
double pi()
Return the value of pi.
Definition: constants.hpp:86
value_of.hpp
stan::VectorView
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
check_consistent_sizes.hpp

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