mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2024-11-16 17:11:53 -05:00
104 lines
3.2 KiB
Plaintext
104 lines
3.2 KiB
Plaintext
[section:logistic_dist Logistic Distribution]
|
|
|
|
``#include <boost/math/distributions/logistic.hpp>``
|
|
|
|
namespace boost{ namespace math{
|
|
|
|
template <class RealType = double,
|
|
class ``__Policy`` = ``__policy_class`` >
|
|
class logistic_distribution;
|
|
|
|
template <class RealType, class Policy>
|
|
class logistic_distribution
|
|
{
|
|
public:
|
|
typedef RealType value_type;
|
|
typedef Policy policy_type;
|
|
// Construct:
|
|
logistic_distribution(RealType location = 0, RealType scale = 1);
|
|
// Accessors:
|
|
RealType location()const; // location.
|
|
RealType scale()const; // scale.
|
|
|
|
};
|
|
|
|
typedef logistic_distribution<> logistic;
|
|
|
|
}} // namespaces
|
|
|
|
The logistic distribution is a continous probability distribution.
|
|
It has two parameters - location and scale. The cumulative distribution
|
|
function of the logistic distribution appears in logistic regression
|
|
and feedforward neural networks. Among other applications,
|
|
United State Chess Federation and FIDE use it to calculate chess ratings.
|
|
|
|
The following graph shows how the distribution changes as the
|
|
parameters change:
|
|
|
|
[graph logistic_pdf]
|
|
|
|
[h4 Member Functions]
|
|
|
|
logistic_distribution(RealType u = 0, RealType s = 1);
|
|
|
|
Constructs a logistic distribution with location /u/ and scale /s/.
|
|
|
|
Requires `scale > 0`, otherwise a __domain_error is raised.
|
|
|
|
RealType location()const;
|
|
|
|
Returns the location of this distribution.
|
|
|
|
RealType scale()const;
|
|
|
|
Returns the scale of this distribution.
|
|
|
|
[h4 Non-member Accessors]
|
|
|
|
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
|
|
that are generic to all distributions are supported: __usual_accessors.
|
|
|
|
The domain of the random variable is \[-\[max_value\], +\[min_value\]\].
|
|
However, the pdf and cdf support inputs of +[infin] and -[infin]
|
|
as special cases if RealType permits.
|
|
|
|
At `p=1` and `p=0`, the quantile function returns the result of
|
|
+__overflow_error and -__overflow_error, while the complement
|
|
quantile function returns the result of -__overflow_error and
|
|
+__overflow_error respectively.
|
|
|
|
[h4 Accuracy]
|
|
|
|
The logistic distribution is implemented in terms of the `std::exp`
|
|
and the `std::log` functions, so its accuracy is related to the
|
|
accurate implementations of those functions on a given platform.
|
|
When calculating the quantile with a non-zero /position/ parameter
|
|
catastrophic cancellation errors can occur:
|
|
in such cases, only a low /absolute error/ can be guaranteed.
|
|
|
|
[h4 Implementation]
|
|
|
|
[table
|
|
[[Function][Implementation Notes]]
|
|
[[pdf][Using the relation: pdf = e[super -(x-u)/s] / (s*(1+e[super -(x-u)/s])[super 2])]]
|
|
[[cdf][Using the relation: p = 1/(1+e[super -(x-u)/s])]]
|
|
[[cdf complement][Using the relation: q = 1/(1+e[super (x-u)/s])]]
|
|
[[quantile][Using the relation: x = u - s*log(1/p-1)]]
|
|
[[quantile from the complement][Using the relation: x = u + s*log(p/1-p)]]
|
|
[[mean][u]]
|
|
[[mode][The same as the mean.]]
|
|
[[skewness][0]]
|
|
[[kurtosis excess][6/5]]
|
|
[[variance][ ([pi]*s)[super 2] / 3]]
|
|
]
|
|
|
|
[endsect]
|
|
|
|
[/ logistic.qbk
|
|
Copyright 2006, 2007 John Maddock and Paul A. Bristow.
|
|
Distributed under the Boost Software License, Version 1.0.
|
|
(See accompanying file LICENSE_1_0.txt or copy at
|
|
http://www.boost.org/LICENSE_1_0.txt).
|
|
]
|
|
|