1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CDF_HPP 23 #include <boost/random/chi_squared_distribution.hpp> 24 #include <boost/random/variate_generator.hpp> 44 template <
typename T_y,
typename T_dof,
typename T_scale>
54 static const char*
function(
"scaled_inv_chi_square_cdf");
58 T_partials_return P(1.0);
66 "Degrees of freedom parameter", nu,
67 "Scale parameter", s);
75 operands_and_partials(y, nu, s);
81 return operands_and_partials.
value(0.0);
88 T_partials_return, T_dof> gamma_vec(stan::length(nu));
90 T_partials_return, T_dof> digamma_vec(stan::length(nu));
94 const T_partials_return half_nu_dbl = 0.5 *
value_of(nu_vec[i]);
95 gamma_vec[i] =
tgamma(half_nu_dbl);
96 digamma_vec[i] =
digamma(half_nu_dbl);
100 for (
size_t n = 0; n < N; n++) {
103 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
107 const T_partials_return y_dbl =
value_of(y_vec[n]);
108 const T_partials_return y_inv_dbl = 1.0 / y_dbl;
109 const T_partials_return half_nu_dbl = 0.5 *
value_of(nu_vec[n]);
110 const T_partials_return s_dbl =
value_of(s_vec[n]);
111 const T_partials_return half_s2_overx_dbl = 0.5 * s_dbl * s_dbl
113 const T_partials_return half_nu_s2_overx_dbl
114 = 2.0 * half_nu_dbl * half_s2_overx_dbl;
116 const T_partials_return Pn =
gamma_q(half_nu_dbl, half_nu_s2_overx_dbl);
117 const T_partials_return gamma_p_deriv =
exp(-half_nu_s2_overx_dbl)
118 *
pow(half_nu_s2_overx_dbl, half_nu_dbl-1) /
tgamma(half_nu_dbl);
123 operands_and_partials.
d_x1[n] += half_nu_s2_overx_dbl * y_inv_dbl
124 * gamma_p_deriv / Pn;
127 operands_and_partials.
d_x2[n]
129 half_nu_s2_overx_dbl,
132 - half_s2_overx_dbl * gamma_p_deriv)
136 operands_and_partials.
d_x3[n]
137 += - 2.0 * half_nu_dbl * s_dbl * y_inv_dbl
138 * gamma_p_deriv / Pn;
143 operands_and_partials.
d_x1[n] *= P;
147 operands_and_partials.
d_x2[n] *= P;
151 operands_and_partials.
d_x3[n] *= P;
153 return operands_and_partials.
value(P);
VectorView< T_return_type, false, true > d_x2
T value_of(const fvar< T > &v)
Return the value of the specified variable.
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_cdf(const T_y &y, const T_dof &nu, const T_scale &s)
The CDF of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter...
size_t length(const std::vector< T > &x)
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
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...
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
size_t max_size(const T1 &x1, const T2 &x2)
VectorBuilder allocates type T1 values to be used as intermediate values.
T grad_reg_inc_gamma(T a, T z, T g, T dig, double precision=1e-6)
Gradient of the regularized incomplete gamma functions igamma(a, z)
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
fvar< T > tgamma(const fvar< T > &x)
Return the result of applying the gamma function to the specified argument.
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.
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
fvar< T > gamma_q(const fvar< T > &x1, const fvar< T > &x2)
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.