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frechet_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_FRECHET_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_FRECHET_CDF_HPP
3
4 #include <boost/random/weibull_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
6 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
7 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
8 #include <stan/math/prim/scal/err/check_nonnegative.hpp>
9 #include <stan/math/prim/scal/err/check_not_nan.hpp>
10 #include <stan/math/prim/scal/err/check_positive.hpp>
11 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
12 #include <stan/math/prim/scal/fun/log1m.hpp>
13 #include <stan/math/prim/scal/fun/multiply_log.hpp>
14 #include <stan/math/prim/scal/fun/value_of.hpp>
15 #include <stan/math/prim/scal/meta/length.hpp>
16 #include <stan/math/prim/scal/meta/is_constant_struct.hpp>
17 #include <stan/math/prim/scal/meta/VectorView.hpp>
18 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
19 #include <stan/math/prim/scal/meta/partials_return_type.hpp>
20 #include <stan/math/prim/scal/meta/return_type.hpp>
21 #include <stan/math/prim/scal/fun/constants.hpp>
22 #include <stan/math/prim/scal/meta/include_summand.hpp>
23 #include <cmath>
24
25 namespace stan {
26
27 namespace math {
28
29 template <typename T_y, typename T_shape, typename T_scale>
30 typename return_type<T_y, T_shape, T_scale>::type
31 frechet_cdf(const T_y& y, const T_shape& alpha, const T_scale& sigma) {
32 typedef typename stan::partials_return_type<T_y, T_shape, T_scale>::type
33 T_partials_return;
34
35 static const char* function("stan::math::frechet_cdf");
36
37 using stan::math::check_positive_finite;
38 using stan::math::check_positive;
39 using stan::math::check_nonnegative;
40 using boost::math::tools::promote_args;
41 using stan::math::value_of;
42 using std::log;
43 using std::exp;
44
45 // check if any vectors are zero length
46 if (!(stan::length(y)
47 && stan::length(alpha)
48 && stan::length(sigma)))
49 return 1.0;
50
51 T_partials_return cdf(1.0);
52 check_positive(function, "Random variable", y);
53 check_positive_finite(function, "Shape parameter", alpha);
54 check_positive_finite(function, "Scale parameter", sigma);
55
56 OperandsAndPartials<T_y, T_shape, T_scale>
57 operands_and_partials(y, alpha, sigma);
58
59 VectorView<const T_y> y_vec(y);
60 VectorView<const T_scale> sigma_vec(sigma);
61 VectorView<const T_shape> alpha_vec(alpha);
62 size_t N = max_size(y, sigma, alpha);
63 for (size_t n = 0; n < N; n++) {
64 const T_partials_return y_dbl = value_of(y_vec[n]);
65 const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
66 const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
67 const T_partials_return pow_ = pow(sigma_dbl / y_dbl, alpha_dbl);
68 const T_partials_return cdf_ = exp(-pow_);
69
70 // cdf
71 cdf *= cdf_;
72
73 // gradients
74 if (!is_constant_struct<T_y>::value)
75 operands_and_partials.d_x1[n] += pow_ * alpha_dbl / y_dbl;
76 if (!is_constant_struct<T_shape>::value)
77 operands_and_partials.d_x2[n] += pow_ * log(y_dbl / sigma_dbl);
78 if (!is_constant_struct<T_scale>::value)
79 operands_and_partials.d_x3[n] -= pow_ * alpha_dbl / sigma_dbl;
80 }
81
82 if (!is_constant_struct<T_y>::value) {
83 for (size_t n = 0; n < stan::length(y); ++n)
84 operands_and_partials.d_x1[n] *= cdf;
85 }
86 if (!is_constant_struct<T_shape>::value) {
87 for (size_t n = 0; n < stan::length(alpha); ++n)
88 operands_and_partials.d_x2[n] *= cdf;
89 }
90 if (!is_constant_struct<T_scale>::value) {
91 for (size_t n = 0; n < stan::length(sigma); ++n)
92 operands_and_partials.d_x3[n] *= cdf;
93 }
94
95 return operands_and_partials.to_var(cdf, y, alpha, sigma);
96 }
97 }
98 }
99 #endif
check_not_nan.hpp
check_positive_finite.hpp
check_positive.hpp
stan::math::value_of
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
stan::math::OperandsAndPartials::to_var
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)
Definition: OperandsAndPartials.hpp:322
return_type.hpp
VectorView.hpp
include_summand.hpp
multiply_log.hpp
stan::math::OperandsAndPartials::d_x1
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Definition: OperandsAndPartials.hpp:253
check_nonnegative.hpp
stan::is_constant_struct
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
Definition: is_constant_struct.hpp:16
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
stan::math::OperandsAndPartials::d_x3
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
Definition: OperandsAndPartials.hpp:259
stan::math::OperandsAndPartials
A variable implementation that stores operands and derivatives with respect to the variable...
Definition: OperandsAndPartials.hpp:238
stan::math::check_positive
bool check_positive(const char *function, const char *name, const T_y &y)
Return true if y is positive.
Definition: check_positive.hpp:68
OperandsAndPartials.hpp
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
VectorBuilder.hpp
log1m.hpp
partials_return_type.hpp
length.hpp
constants.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
Definition: OperandsAndPartials.hpp:256
is_constant_struct.hpp
stan::math::pow
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
stan::math::check_nonnegative
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
Definition: check_nonnegative.hpp:66
value_of.hpp
stan::math::frechet_cdf
return_type< T_y, T_shape, T_scale >::type frechet_cdf(const T_y &y, const T_shape &alpha, const T_scale &sigma)
Definition: frechet_cdf.hpp:31
stan::VectorView
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
stan::partials_return_type::type
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
Definition: partials_return_type.hpp:26
check_consistent_sizes.hpp
stan::math::check_positive_finite
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
Definition: check_positive_finite.hpp:28

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