1 #ifndef STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_CDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_CDF_HPP 22 #include <boost/random/student_t_distribution.hpp> 23 #include <boost/random/variate_generator.hpp> 30 template <
typename T_y,
typename T_dof,
typename T_loc,
typename T_scale>
33 const T_scale& sigma) {
42 static const char*
function(
"student_t_cdf");
46 T_partials_return P(1.0);
57 size_t N =
max_size(y, nu, mu, sigma);
60 operands_and_partials(y, nu, mu, sigma);
65 if (
value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
66 return operands_and_partials.
value(0.0);
72 T_partials_return digammaHalf = 0;
75 T_partials_return, T_dof>
76 digamma_vec(stan::length(nu));
78 T_partials_return, T_dof>
79 digammaNu_vec(stan::length(nu));
81 T_partials_return, T_dof>
82 digammaNuPlusHalf_vec(stan::length(nu));
88 const T_partials_return nu_dbl =
value_of(nu_vec[i]);
90 digammaNu_vec[i] =
digamma(0.5 * nu_dbl);
91 digammaNuPlusHalf_vec[i] =
digamma(0.5 + 0.5 * nu_dbl);
95 for (
size_t n = 0; n < N; n++) {
98 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
102 const T_partials_return sigma_inv = 1.0 /
value_of(sigma_vec[n]);
105 const T_partials_return nu_dbl =
value_of(nu_vec[n]);
106 const T_partials_return q = nu_dbl / (t * t);
107 const T_partials_return r = 1.0 / (1.0 + q);
108 const T_partials_return J = 2 * r * r * q / t;
109 const T_partials_return betaNuHalf =
exp(
lbeta(0.5, 0.5*nu_dbl));
110 double zJacobian = t > 0 ? - 0.5 : 0.5;
113 T_partials_return z =
inc_beta(0.5 * nu_dbl, (T_partials_return)0.5,
115 const T_partials_return Pn = t > 0 ? 1.0 - 0.5 * z : 0.5 * z;
116 const T_partials_return d_ibeta =
pow(r, -0.5)
117 *
pow(1.0 - r, 0.5*nu_dbl - 1) / betaNuHalf;
122 operands_and_partials.
d_x1[n]
123 += - zJacobian * d_ibeta * J * sigma_inv / Pn;
125 T_partials_return g1 = 0;
126 T_partials_return g2 = 0;
129 (T_partials_return)0.5, 1.0 - r,
130 digammaNu_vec[n], digammaHalf,
131 digammaNuPlusHalf_vec[n],
134 operands_and_partials.
d_x2[n]
135 += zJacobian * (d_ibeta * (r / t) * (r / t) + 0.5 * g1) / Pn;
139 operands_and_partials.
d_x3[n]
140 += zJacobian * d_ibeta * J * sigma_inv / Pn;
142 operands_and_partials.
d_x4[n]
143 += zJacobian * d_ibeta * J * sigma_inv * t / Pn;
146 T_partials_return z = 1.0 -
inc_beta((T_partials_return)0.5,
151 const T_partials_return Pn = t > 0 ? 1.0 - 0.5 * z : 0.5 * z;
153 T_partials_return d_ibeta =
pow(1.0-r, 0.5*nu_dbl-1) *
pow(r, -0.5)
159 operands_and_partials.
d_x1[n]
160 += zJacobian * d_ibeta * J * sigma_inv / Pn;
162 T_partials_return g1 = 0;
163 T_partials_return g2 = 0;
167 digammaHalf, digammaNu_vec[n],
168 digammaNuPlusHalf_vec[n],
171 operands_and_partials.
d_x2[n]
172 += zJacobian * (- d_ibeta * (r / t) * (r / t) + 0.5 * g2) / Pn;
175 operands_and_partials.
d_x3[n]
176 += - zJacobian * d_ibeta * J * sigma_inv / Pn;
178 operands_and_partials.
d_x4[n]
179 += - zJacobian * d_ibeta * J * sigma_inv * t / Pn;
185 operands_and_partials.
d_x1[n] *= P;
189 operands_and_partials.
d_x2[n] *= P;
193 operands_and_partials.
d_x3[n] *= P;
197 operands_and_partials.
d_x4[n] *= P;
199 return operands_and_partials.
value(P);
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.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
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)
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...
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_cdf(const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
void grad_reg_inc_beta(T &g1, T &g2, const T &a, const T &b, const T &z, const T &digammaA, const T &digammaB, const T &digammaSum, const T &betaAB)
Computes the gradients of the regularized incomplete beta function.
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)
VectorBuilder allocates type T1 values to be used as intermediate values.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
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[].
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
VectorView< T_return_type, false, true > d_x4