1 #ifndef STAN_MATH_PRIM_SCAL_PROB_POISSON_CDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_POISSON_CDF_HPP 17 #include <boost/random/poisson_distribution.hpp> 18 #include <boost/random/variate_generator.hpp> 26 template <
typename T_n,
typename T_rate>
29 static const char*
function(
"poisson_cdf");
36 T_partials_return P(1.0);
42 "Rate parameter", lambda);
58 return operands_and_partials.
value(0.0);
61 for (
size_t i = 0; i <
size; i++) {
67 const T_partials_return n_dbl =
value_of(n_vec[i]);
68 const T_partials_return lambda_dbl =
value_of(lambda_vec[i]);
69 const T_partials_return Pi =
gamma_q(n_dbl+1, lambda_dbl);
74 operands_and_partials.
d_x1[i] -=
exp(-lambda_dbl)
75 *
pow(lambda_dbl, n_dbl) /
tgamma(n_dbl+1) / Pi;
80 operands_and_partials.
d_x1[i] *= P;
82 return operands_and_partials.
value(P);
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.
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...
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.
return_type< T_rate >::type poisson_cdf(const T_n &n, const T_rate &lambda)
size_t max_size(const T1 &x1, const T2 &x2)
int max(const std::vector< int > &x)
Returns the maximum coefficient in the specified column vector.
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
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.
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