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binomial_ccdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_CCDF_LOG_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  template <typename T_n, typename T_N, typename T_prob>
30  typename return_type<T_prob>::type
31  binomial_ccdf_log(const T_n& n, const T_N& N, const T_prob& theta) {
32  static const char* function("stan::math::binomial_ccdf_log");
34  T_partials_return;
35 
42 
43  // Ensure non-zero arguments lenghts
44  if (!(stan::length(n) && stan::length(N) && stan::length(theta)))
45  return 0.0;
46 
47  T_partials_return P(0.0);
48 
49  // Validate arguments
50  check_nonnegative(function, "Population size parameter", N);
51  check_finite(function, "Probability parameter", theta);
52  check_bounded(function, "Probability parameter", theta, 0.0, 1.0);
53  check_consistent_sizes(function,
54  "Successes variable", n,
55  "Population size parameter", N,
56  "Probability parameter", theta);
57 
58  // Wrap arguments in vector views
59  VectorView<const T_n> n_vec(n);
60  VectorView<const T_N> N_vec(N);
61  VectorView<const T_prob> theta_vec(theta);
62  size_t size = max_size(n, N, theta);
63 
64  // Compute vectorized cdf_log and gradient
67  using stan::math::lbeta;
68  using std::exp;
69  using std::pow;
70  using std::log;
71  using std::exp;
72 
73  OperandsAndPartials<T_prob> operands_and_partials(theta);
74 
75  // Explicit return for extreme values
76  // The gradients are technically ill-defined,
77  // but treated as negative infinity
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  return operands_and_partials.to_var(stan::math::negative_infinity(),
88  theta);
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 = 1.0 - inc_beta(N_dbl - n_dbl, n_dbl + 1,
95  1 - theta_dbl);
96 
97  P += log(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 
104  return operands_and_partials.to_var(P, theta);
105  }
106  }
107 }
108 #endif
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
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
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
return_type< T_prob >::type binomial_ccdf_log(const T_n &n, const T_N &N, const T_prob &theta)
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
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:132

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