Stan Math Library  2.15.0
reverse mode automatic differentiation
weibull_lpdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_WEIBULL_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_WEIBULL_LPDF_HPP
3 
19 #include <boost/random/weibull_distribution.hpp>
20 #include <boost/random/variate_generator.hpp>
21 #include <cmath>
22 
23 namespace stan {
24  namespace math {
25 
40  template <bool propto,
41  typename T_y, typename T_shape, typename T_scale>
43  weibull_lpdf(const T_y& y, const T_shape& alpha, const T_scale& sigma) {
44  static const char* function("weibull_lpdf");
46  T_partials_return;
47 
48  using std::log;
49 
50  if (!(stan::length(y)
51  && stan::length(alpha)
52  && stan::length(sigma)))
53  return 0.0;
54 
55  T_partials_return logp(0.0);
56  check_finite(function, "Random variable", y);
57  check_positive_finite(function, "Shape parameter", alpha);
58  check_positive_finite(function, "Scale parameter", sigma);
59  check_consistent_sizes(function,
60  "Random variable", y,
61  "Shape parameter", alpha,
62  "Scale parameter", sigma);
63 
65  return 0.0;
66 
68  scalar_seq_view<const T_shape> alpha_vec(alpha);
69  scalar_seq_view<const T_scale> sigma_vec(sigma);
70  size_t N = max_size(y, alpha, sigma);
71 
72  for (size_t n = 0; n < N; n++) {
73  const T_partials_return y_dbl = value_of(y_vec[n]);
74  if (y_dbl < 0)
75  return LOG_ZERO;
76  }
77 
79  T_partials_return, T_shape> log_alpha(length(alpha));
80  for (size_t i = 0; i < length(alpha); i++)
82  log_alpha[i] = log(value_of(alpha_vec[i]));
83 
85  T_partials_return, T_y> log_y(length(y));
86  for (size_t i = 0; i < length(y); i++)
88  log_y[i] = log(value_of(y_vec[i]));
89 
91  T_partials_return, T_scale> log_sigma(length(sigma));
92  for (size_t i = 0; i < length(sigma); i++)
94  log_sigma[i] = log(value_of(sigma_vec[i]));
95 
97  T_partials_return, T_scale> inv_sigma(length(sigma));
98  for (size_t i = 0; i < length(sigma); i++)
100  inv_sigma[i] = 1.0 / value_of(sigma_vec[i]);
101 
103  T_partials_return, T_y, T_shape, T_scale>
104  y_div_sigma_pow_alpha(N);
105  for (size_t i = 0; i < N; i++)
107  const T_partials_return y_dbl = value_of(y_vec[i]);
108  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
109  y_div_sigma_pow_alpha[i] = pow(y_dbl * inv_sigma[i], alpha_dbl);
110  }
111 
113  operands_and_partials(y, alpha, sigma);
114  for (size_t n = 0; n < N; n++) {
115  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
117  logp += log_alpha[n];
119  logp += (alpha_dbl-1.0)*log_y[n];
121  logp -= alpha_dbl*log_sigma[n];
123  logp -= y_div_sigma_pow_alpha[n];
124 
126  const T_partials_return inv_y = 1.0 / value_of(y_vec[n]);
127  operands_and_partials.d_x1[n]
128  += (alpha_dbl-1.0) * inv_y
129  - alpha_dbl * y_div_sigma_pow_alpha[n] * inv_y;
130  }
132  operands_and_partials.d_x2[n]
133  += 1.0/alpha_dbl
134  + (1.0 - y_div_sigma_pow_alpha[n]) * (log_y[n] - log_sigma[n]);
136  operands_and_partials.d_x3[n]
137  += alpha_dbl * inv_sigma[n] * (y_div_sigma_pow_alpha[n] - 1.0);
138  }
139  return operands_and_partials.value(logp);
140  }
141 
142  template <typename T_y, typename T_shape, typename T_scale>
143  inline
145  weibull_lpdf(const T_y& y, const T_shape& alpha, const T_scale& sigma) {
146  return weibull_lpdf<false>(y, alpha, sigma);
147  }
148 
149  }
150 }
151 #endif
VectorView< T_return_type, false, true > d_x2
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
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)
Definition: length.hpp:10
const double LOG_ZERO
Definition: constants.hpp:172
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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
Definition: return_type.hpp:27
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
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)
Definition: max_size.hpp:9
VectorBuilder allocates type T1 values to be used as intermediate values.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
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.
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
return_type< T_y, T_shape, T_scale >::type weibull_lpdf(const T_y &y, const T_shape &alpha, const T_scale &sigma)
Returns the Weibull log probability density for the given location and scale.
VectorView< T_return_type, false, true > d_x1

     [ Stan Home Page ] © 2011–2016, Stan Development Team.