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