1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_CDF_HPP
17 #include <boost/random/chi_squared_distribution.hpp>
18 #include <boost/random/variate_generator.hpp>
35 template <
typename T_y,
typename T_dof>
36 typename return_type<T_y, T_dof>::type
38 static const char*
function(
"stan::math::chi_square_cdf");
48 T_partials_return cdf(1.0);
59 "Degrees of freedom parameter", nu);
67 operands_and_partials(y, nu);
73 return operands_and_partials.
to_var(0.0, y, nu);
86 T_partials_return, T_dof> gamma_vec(stan::length(nu));
88 T_partials_return, T_dof> digamma_vec(stan::length(nu));
92 const T_partials_return alpha_dbl =
value_of(nu_vec[i]) * 0.5;
93 gamma_vec[i] =
tgamma(alpha_dbl);
94 digamma_vec[i] =
digamma(alpha_dbl);
99 for (
size_t n = 0; n < N; n++) {
102 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
106 const T_partials_return y_dbl =
value_of(y_vec[n]);
107 const T_partials_return alpha_dbl =
value_of(nu_vec[n]) * 0.5;
108 const T_partials_return beta_dbl = 0.5;
111 const T_partials_return Pn =
gamma_p(alpha_dbl, beta_dbl * y_dbl);
116 operands_and_partials.
d_x1[n] += beta_dbl *
exp(-beta_dbl * y_dbl)
117 *
pow(beta_dbl * y_dbl, alpha_dbl-1) /
tgamma(alpha_dbl) / Pn;
119 operands_and_partials.
d_x2[n]
121 * y_dbl, gamma_vec[n],
122 digamma_vec[n]) / Pn;
127 operands_and_partials.
d_x1[n] *= cdf;
131 operands_and_partials.
d_x2[n] *= cdf;
134 return operands_and_partials.
to_var(cdf, y, nu);
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.
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)
A variable implementation that stores operands and derivatives with respect to the variable...
size_t max_size(const T1 &x1, const T2 &x2)
fvar< T > gamma_p(const fvar< T > &x1, const fvar< T > &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
return_type< T_y, T_dof >::type chi_square_cdf(const T_y &y, const T_dof &nu)
Calculates the chi square cumulative distribution function for the given variate and degrees of freed...
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
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)