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binomial_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_CDF_HPP
3 
4 #include <boost/random/binomial_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
23 #include <cmath>
24 
25 namespace stan {
26 
27  namespace math {
28 
29  // Binomial CDF
30  template <typename T_n, typename T_N, typename T_prob>
31  typename return_type<T_prob>::type
32  binomial_cdf(const T_n& n, const T_N& N, const T_prob& theta) {
33  static const char* function("stan::math::binomial_cdf");
35  T_partials_return;
36 
43 
44  // Ensure non-zero arguments lenghts
45  if (!(stan::length(n) && stan::length(N) && stan::length(theta)))
46  return 1.0;
47 
48  T_partials_return P(1.0);
49 
50  // Validate arguments
51  check_nonnegative(function, "Population size parameter", N);
52  check_finite(function, "Probability parameter", theta);
53  check_bounded(function, "Probability parameter", theta, 0.0, 1.0);
54  check_consistent_sizes(function,
55  "Successes variable", n,
56  "Population size parameter", N,
57  "Probability parameter", theta);
58 
59 
60  // Wrap arguments in vector views
61  VectorView<const T_n> n_vec(n);
62  VectorView<const T_N> N_vec(N);
63  VectorView<const T_prob> theta_vec(theta);
64  size_t size = max_size(n, N, theta);
65 
66  // Compute vectorized CDF and gradient
69  using stan::math::lbeta;
70  using std::exp;
71  using std::pow;
72  using std::exp;
73 
74  OperandsAndPartials<T_prob> operands_and_partials(theta);
75 
76  // Explicit return for extreme values
77  // The gradients are technically ill-defined, but treated as zero
78  for (size_t i = 0; i < stan::length(n); i++) {
79  if (value_of(n_vec[i]) < 0)
80  return operands_and_partials.to_var(0.0, theta);
81  }
82 
83  for (size_t i = 0; i < size; i++) {
84  // Explicit results for extreme values
85  // The gradients are technically ill-defined, but treated as zero
86  if (value_of(n_vec[i]) >= value_of(N_vec[i])) {
87  continue;
88  }
89 
90  const T_partials_return n_dbl = value_of(n_vec[i]);
91  const T_partials_return N_dbl = value_of(N_vec[i]);
92  const T_partials_return theta_dbl = value_of(theta_vec[i]);
93  const T_partials_return betafunc = exp(lbeta(N_dbl-n_dbl, n_dbl+1));
94  const T_partials_return Pi = inc_beta(N_dbl - n_dbl, n_dbl + 1,
95  1 - theta_dbl);
96 
97  P *= Pi;
98 
100  operands_and_partials.d_x1[i] -= pow(theta_dbl, n_dbl)
101  * pow(1-theta_dbl, N_dbl-n_dbl-1) / betafunc / Pi;
102  }
103 
105  for (size_t i = 0; i < stan::length(theta); ++i)
106  operands_and_partials.d_x1[i] *= P;
107  }
108 
109  return operands_and_partials.to_var(P, theta);
110  }
111 
112  }
113 }
114 #endif
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.
Definition: value_of.hpp:16
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:16
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
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.
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)
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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 > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:20
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
A variable implementation that stores operands and derivatives with respect to the variable...
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
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.
Definition: size.hpp:17
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)
Definition: pow.hpp:18
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
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

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