1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_LCDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_LCDF_HPP 25 #include <boost/math/special_functions/gamma.hpp> 26 #include <boost/random/gamma_distribution.hpp> 27 #include <boost/random/variate_generator.hpp> 49 template <
typename T_y,
typename T_scale_succ,
typename T_scale_fail>
52 const T_scale_fail& beta) {
61 static const char*
function(
"beta_lcdf");
63 using boost::math::tools::promote_args;
65 T_partials_return cdf_log(0.0);
74 "First shape parameter", alpha,
75 "Second shape parameter", beta);
83 operands_and_partials(y, alpha, beta);
92 T_partials_return, T_scale_succ, T_scale_fail>
93 digamma_alpha_vec(
max_size(alpha, beta));
97 T_partials_return, T_scale_succ, T_scale_fail>
98 digamma_beta_vec(
max_size(alpha, beta));
101 T_scale_fail>::value,
102 T_partials_return, T_scale_succ, T_scale_fail>
103 digamma_sum_vec(
max_size(alpha, beta));
106 for (
size_t i = 0; i < N; i++) {
107 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
108 const T_partials_return beta_dbl =
value_of(beta_vec[i]);
110 digamma_alpha_vec[i] =
digamma(alpha_dbl);
111 digamma_beta_vec[i] =
digamma(beta_dbl);
112 digamma_sum_vec[i] =
digamma(alpha_dbl + beta_dbl);
116 for (
size_t n = 0; n < N; n++) {
117 const T_partials_return y_dbl =
value_of(y_vec[n]);
118 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
119 const T_partials_return beta_dbl =
value_of(beta_vec[n]);
120 const T_partials_return betafunc_dbl =
exp(
lbeta(alpha_dbl, beta_dbl));
121 const T_partials_return Pn =
inc_beta(alpha_dbl, beta_dbl, y_dbl);
126 operands_and_partials.
d_x1[n] +=
pow(1-y_dbl, beta_dbl-1)
127 *
pow(y_dbl, alpha_dbl-1) / betafunc_dbl / Pn;
129 T_partials_return g1 = 0;
130 T_partials_return g2 = 0;
134 digamma_alpha_vec[n],
135 digamma_beta_vec[n], digamma_sum_vec[n],
139 operands_and_partials.
d_x2[n] += g1 / Pn;
141 operands_and_partials.
d_x3[n] += g2 / Pn;
144 return operands_and_partials.
value(cdf_log);
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.
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
fvar< T > log(const fvar< T > &x)
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 > 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 grad_reg_inc_beta(T &g1, T &g2, const T &a, const T &b, const T &z, const T &digammaA, const T &digammaB, const T &digammaSum, const T &betaAB)
Computes the gradients of the regularized incomplete beta function.
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.
VectorView< T_return_type, false, true > d_x3
size_t max_size(const T1 &x1, const T2 &x2)
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_lcdf(const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
Returns the beta log cumulative distribution function for the given probability, success, and failure parameters.
VectorBuilder allocates type T1 values to be used as intermediate values.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
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.