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
4 #include <boost/random/chi_squared_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
44 template <
typename T_y,
typename T_dof,
typename T_scale>
45 typename return_type<T_y, T_dof, T_scale>::type
55 static const char*
function(
"stan::math::scaled_inv_chi_square_cdf");
64 T_partials_return P(1.0);
72 "Degrees of freedom parameter", nu,
73 "Scale parameter", s);
82 operands_and_partials(y, nu, s);
89 return operands_and_partials.
to_var(0.0, y, nu, s);
101 T_partials_return, T_dof> gamma_vec(stan::length(nu));
103 T_partials_return, T_dof> digamma_vec(stan::length(nu));
107 const T_partials_return half_nu_dbl = 0.5 *
value_of(nu_vec[i]);
108 gamma_vec[i] =
tgamma(half_nu_dbl);
109 digamma_vec[i] =
digamma(half_nu_dbl);
114 for (
size_t n = 0; n < N; n++) {
117 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
122 const T_partials_return y_dbl =
value_of(y_vec[n]);
123 const T_partials_return y_inv_dbl = 1.0 / y_dbl;
124 const T_partials_return half_nu_dbl = 0.5 *
value_of(nu_vec[n]);
125 const T_partials_return s_dbl =
value_of(s_vec[n]);
126 const T_partials_return half_s2_overx_dbl = 0.5 * s_dbl * s_dbl
128 const T_partials_return half_nu_s2_overx_dbl
129 = 2.0 * half_nu_dbl * half_s2_overx_dbl;
132 const T_partials_return Pn =
gamma_q(half_nu_dbl, half_nu_s2_overx_dbl);
133 const T_partials_return gamma_p_deriv =
exp(-half_nu_s2_overx_dbl)
134 *
pow(half_nu_s2_overx_dbl, half_nu_dbl-1) /
tgamma(half_nu_dbl);
139 operands_and_partials.
d_x1[n] += half_nu_s2_overx_dbl * y_inv_dbl
140 * gamma_p_deriv / Pn;
145 operands_and_partials.
d_x2[n]
147 half_nu_s2_overx_dbl,
150 - half_s2_overx_dbl * gamma_p_deriv)
154 operands_and_partials.
d_x3[n]
155 += - 2.0 * half_nu_dbl * s_dbl * y_inv_dbl
156 * gamma_p_deriv / Pn;
161 operands_and_partials.
d_x1[n] *= P;
165 operands_and_partials.
d_x2[n] *= P;
169 operands_and_partials.
d_x3[n] *= P;
172 return operands_and_partials.
to_var(P, y, nu, s);
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.
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)
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)
T grad_reg_inc_gamma(T a, T z, T g, T dig, T precision=1e-6)
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
fvar< T > exp(const fvar< T > &x)
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
A variable implementation that stores operands and derivatives with respect to the variable...
size_t max_size(const T1 &x1, const T2 &x2)
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
fvar< T > tgamma(const fvar< T > &x)
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
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)
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
fvar< T > digamma(const fvar< T > &x)