1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_CDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_CDF_HPP 26 #include <boost/math/special_functions/gamma.hpp> 27 #include <boost/random/gamma_distribution.hpp> 28 #include <boost/random/variate_generator.hpp> 46 template <
typename T_y,
typename T_scale_succ,
typename T_scale_fail>
48 beta_cdf(
const T_y& y,
const T_scale_succ& alpha,
49 const T_scale_fail& beta) {
58 static const char*
function(
"beta_cdf");
59 using boost::math::tools::promote_args;
61 T_partials_return P(1.0);
68 "First shape parameter", alpha,
69 "Second shape parameter", beta);
79 operands_and_partials(y, alpha, beta);
85 return operands_and_partials.
value(0.0);
90 T_partials_return, T_scale_succ, T_scale_fail>
91 digamma_alpha_vec(
max_size(alpha, beta));
95 T_partials_return, T_scale_succ, T_scale_fail>
96 digamma_beta_vec(
max_size(alpha, beta));
100 T_partials_return, T_scale_succ, T_scale_fail>
101 digamma_sum_vec(
max_size(alpha, beta));
104 for (
size_t n = 0; n < N; n++) {
105 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
106 const T_partials_return beta_dbl =
value_of(beta_vec[n]);
108 digamma_alpha_vec[n] =
digamma(alpha_dbl);
109 digamma_beta_vec[n] =
digamma(beta_dbl);
110 digamma_sum_vec[n] =
digamma(alpha_dbl + beta_dbl);
114 for (
size_t n = 0; n < N; n++) {
117 if (
value_of(y_vec[n]) >= 1.0)
continue;
119 const T_partials_return y_dbl =
value_of(y_vec[n]);
120 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
121 const T_partials_return beta_dbl =
value_of(beta_vec[n]);
123 const T_partials_return Pn =
inc_beta(alpha_dbl, beta_dbl, y_dbl);
128 operands_and_partials.
d_x1[n]
132 operands_and_partials.
d_x2[n]
134 digamma_alpha_vec[n], digamma_sum_vec[n]) / Pn;
136 operands_and_partials.
d_x3[n]
138 digamma_beta_vec[n], digamma_sum_vec[n]) / Pn;
143 operands_and_partials.
d_x1[n] *= P;
147 operands_and_partials.
d_x2[n] *= P;
151 operands_and_partials.
d_x3[n] *= P;
154 return operands_and_partials.
value(P);
VectorView< T_return_type, false, true > d_x2
void check_less_or_equal(const char *function, const char *name, const T_y &y, const T_high &high)
Check if y is less or equal to high.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
T inc_beta_dda(T a, T b, T z, T digamma_a, T digamma_ab)
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to a.
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)
T inc_beta_ddb(T a, T b, T z, T digamma_b, T digamma_ab)
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to b.
T inc_beta_ddz(T a, T b, T z)
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to z.
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 > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_cdf(const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
Calculates the beta cumulative distribution function for the given variate and scale variables...
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)
VectorBuilder allocates type T1 values to be used as intermediate values.
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[].
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.
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.