1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_CDF_HPP
23 #include <boost/random/binomial_distribution.hpp>
24 #include <boost/random/variate_generator.hpp>
32 template <
typename T_n,
typename T_N,
typename T_prob>
33 typename return_type<T_prob>::type
35 static const char*
function(
"stan::math::binomial_cdf");
50 T_partials_return P(1.0);
55 check_bounded(
function,
"Probability parameter", theta, 0.0, 1.0);
57 "Successes variable", n,
58 "Population size parameter", N,
59 "Probability parameter", theta);
82 return operands_and_partials.
value(0.0);
85 for (
size_t i = 0; i <
size; i++) {
92 const T_partials_return n_dbl =
value_of(n_vec[i]);
93 const T_partials_return N_dbl =
value_of(N_vec[i]);
94 const T_partials_return theta_dbl =
value_of(theta_vec[i]);
95 const T_partials_return betafunc =
exp(
lbeta(N_dbl-n_dbl, n_dbl+1));
96 const T_partials_return Pi =
inc_beta(N_dbl - n_dbl, n_dbl + 1,
102 operands_and_partials.
d_x1[i] -=
pow(theta_dbl, n_dbl)
103 *
pow(1-theta_dbl, N_dbl-n_dbl-1) / betafunc / Pi;
108 operands_and_partials.
d_x1[i] *= P;
111 return operands_and_partials.
value(P);
return_type< T_prob >::type binomial_cdf(const T_n &n, const T_N &N, const T_prob &theta)
T value_of(const fvar< T > &v)
Return the value of the specified variable.
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
size_t length(const std::vector< T > &x)
bool check_bounded(const char *function, const char *name, const T_y &y, const T_low &low, const T_high &high)
Return true if the value is between the low and high values, inclusively.
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
fvar< T > exp(const fvar< T > &x)
This class builds partial derivatives with respect to a set of operands.
size_t max_size(const T1 &x1, const T2 &x2)
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
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.
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.
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[].
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
VectorView< T_return_type, false, true > d_x1