1 #ifndef STAN_MATH_PRIM_SCAL_PROB_GAMMA_LCCDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_GAMMA_LCCDF_HPP 24 #include <boost/random/gamma_distribution.hpp> 25 #include <boost/random/variate_generator.hpp> 32 template <
typename T_y,
typename T_shape,
typename T_inv_scale>
35 const T_inv_scale& beta) {
43 static const char*
function(
"gamma_lccdf");
45 using boost::math::tools::promote_args;
48 T_partials_return P(0.0);
56 "Shape parameter", alpha,
57 "Scale Parameter", beta);
65 operands_and_partials(y, alpha, beta);
71 return operands_and_partials.
value(0.0);
80 T_partials_return, T_shape> gamma_vec(stan::length(alpha));
82 T_partials_return, T_shape>
83 digamma_vec(stan::length(alpha));
87 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
88 gamma_vec[i] =
tgamma(alpha_dbl);
89 digamma_vec[i] =
digamma(alpha_dbl);
93 for (
size_t n = 0; n < N; n++) {
96 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
99 const T_partials_return y_dbl =
value_of(y_vec[n]);
100 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
101 const T_partials_return beta_dbl =
value_of(beta_vec[n]);
103 const T_partials_return Pn =
gamma_q(alpha_dbl, beta_dbl * y_dbl);
108 operands_and_partials.
d_x1[n] -= beta_dbl *
exp(-beta_dbl * y_dbl)
109 *
pow(beta_dbl * y_dbl, alpha_dbl-1) /
tgamma(alpha_dbl) / Pn;
111 operands_and_partials.
d_x2[n]
113 * y_dbl, gamma_vec[n],
114 digamma_vec[n]) / Pn;
116 operands_and_partials.
d_x3[n] -= y_dbl *
exp(-beta_dbl * y_dbl)
117 *
pow(beta_dbl * y_dbl, alpha_dbl-1) /
tgamma(alpha_dbl) / Pn;
119 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.
fvar< T > log(const fvar< T > &x)
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
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)
T grad_reg_inc_gamma(T a, T z, T g, T dig, double precision=1e-6, int max_steps=1e5)
Gradient of the regularized incomplete gamma functions igamma(a, z)
VectorBuilder allocates type T1 values to be used as intermediate values.
return_type< T_y, T_shape, T_inv_scale >::type gamma_lccdf(const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
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.
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.
fvar< T > gamma_q(const fvar< T > &x1, const fvar< T > &x2)
VectorView< T_return_type, false, true > d_x1
double negative_infinity()
Return negative infinity.
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.