projects / ceph.git / blame
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|---|---|---|
| 7c673cae FG |
1 | [section:logistic_dist Logistic Distribution] |
| 2 | ||
| 3 | ``#include <boost/math/distributions/logistic.hpp>`` | |
| 4 | ||
| 5 | namespace boost{ namespace math{ | |
| 6 | ||
| 7 | template <class RealType = double, | |
| 8 | class ``__Policy`` = ``__policy_class`` > | |
| 9 | class logistic_distribution; | |
| 10 | ||
| 11 | template <class RealType, class Policy> | |
| 12 | class logistic_distribution | |
| 13 | { | |
| 14 | public: | |
| 15 | typedef RealType value_type; | |
| 16 | typedef Policy policy_type; | |
| 17 | // Construct: | |
| 18 | logistic_distribution(RealType location = 0, RealType scale = 1); | |
| 19 | // Accessors: | |
| 20 | RealType location()const; // location. | |
| 21 | RealType scale()const; // scale. | |
| 22 | ||
| 23 | }; | |
| 24 | ||
| 25 | typedef logistic_distribution<> logistic; | |
| 26 | ||
| 27 | }} // namespaces | |
| 28 | ||
| 29 | The logistic distribution is a continous probability distribution. | |
| 30 | It has two parameters - location and scale. The cumulative distribution | |
| 31 | function of the logistic distribution appears in logistic regression | |
| 32 | and feedforward neural networks. Among other applications, | |
| 33 | United State Chess Federation and FIDE use it to calculate chess ratings. | |
| 34 | ||
| 35 | The following graph shows how the distribution changes as the | |
| 36 | parameters change: | |
| 37 | ||
| 38 | [graph logistic_pdf] | |
| 39 | ||
| 40 | [h4 Member Functions] | |
| 41 | ||
| 42 | logistic_distribution(RealType u = 0, RealType s = 1); | |
| 43 | ||
| 44 | Constructs a logistic distribution with location /u/ and scale /s/. | |
| 45 | ||
| 46 | Requires `scale > 0`, otherwise a __domain_error is raised. | |
| 47 | ||
| 48 | RealType location()const; | |
| 49 | ||
| 50 | Returns the location of this distribution. | |
| 51 | ||
| 52 | RealType scale()const; | |
| 53 | ||
| 54 | Returns the scale of this distribution. | |
| 55 | ||
| 56 | [h4 Non-member Accessors] | |
| 57 | ||
| 58 | All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions] | |
| 59 | that are generic to all distributions are supported: __usual_accessors. | |
| 60 | ||
| 61 | The domain of the random variable is \[-\[max_value\], +\[min_value\]\]. | |
| 62 | However, the pdf and cdf support inputs of +[infin] and -[infin] | |
| 63 | as special cases if RealType permits. | |
| 64 | ||
| 65 | At `p=1` and `p=0`, the quantile function returns the result of | |
| 66 | +__overflow_error and -__overflow_error, while the complement | |
| 67 | quantile function returns the result of -__overflow_error and | |
| 68 | +__overflow_error respectively. | |
| 69 | ||
| 70 | [h4 Accuracy] | |
| 71 | ||
| 72 | The logistic distribution is implemented in terms of the `std::exp` | |
| 73 | and the `std::log` functions, so its accuracy is related to the | |
| 74 | accurate implementations of those functions on a given platform. | |
| 75 | When calculating the quantile with a non-zero /position/ parameter | |
| 76 | catastrophic cancellation errors can occur: | |
| 77 | in such cases, only a low /absolute error/ can be guaranteed. | |
| 78 | ||
| 79 | [h4 Implementation] | |
| 80 | ||
| 81 | [table | |
| 82 | [[Function][Implementation Notes]] | |
| 83 | [[pdf][Using the relation: pdf = e[super -(x-u)/s] / (s*(1+e[super -(x-u)/s])[super 2])]] | |
| 84 | [[cdf][Using the relation: p = 1/(1+e[super -(x-u)/s])]] | |
| 85 | [[cdf complement][Using the relation: q = 1/(1+e[super (x-u)/s])]] | |
| 86 | [[quantile][Using the relation: x = u - s*log(1/p-1)]] | |
| 87 | [[quantile from the complement][Using the relation: x = u + s*log(p/1-p)]] | |
| 88 | [[mean][u]] | |
| 89 | [[mode][The same as the mean.]] | |
| 90 | [[skewness][0]] | |
| 91 | [[kurtosis excess][6/5]] | |
| 92 | [[variance][ ([pi]*s)[super 2] / 3]] | |
| 93 | ] | |
| 94 | ||
| 95 | [endsect] | |
| 96 | ||
| 97 | [/ logistic.qbk | |
| 98 | Copyright 2006, 2007 John Maddock and Paul A. Bristow. | |
| 99 | Distributed under the Boost Software License, Version 1.0. | |
| 100 | (See accompanying file LICENSE_1_0.txt or copy at | |
| 101 | http://www.boost.org/LICENSE_1_0.txt). | |
| 102 | ] | |
| 103 |