mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2024-11-17 17:42:02 -05:00
109 lines
3.5 KiB
Plaintext
109 lines
3.5 KiB
Plaintext
[section:exp_dist Exponential Distribution]
|
|
|
|
``#include <boost/math/distributions/exponential.hpp>``
|
|
|
|
template <class RealType = double,
|
|
class ``__Policy`` = ``__policy_class`` >
|
|
class exponential_distribution;
|
|
|
|
typedef exponential_distribution<> exponential;
|
|
|
|
template <class RealType, class ``__Policy``>
|
|
class exponential_distribution
|
|
{
|
|
public:
|
|
typedef RealType value_type;
|
|
typedef Policy policy_type;
|
|
|
|
exponential_distribution(RealType lambda = 1);
|
|
|
|
RealType lambda()const;
|
|
};
|
|
|
|
|
|
The [@http://en.wikipedia.org/wiki/Exponential_distribution exponential distribution]
|
|
is a [@http://en.wikipedia.org/wiki/Probability_distribution continuous probability distribution]
|
|
with PDF:
|
|
|
|
[equation exponential_dist_ref1]
|
|
|
|
It is often used to model the time between independent
|
|
events that happen at a constant average rate.
|
|
|
|
The following graph shows how the distribution changes for different
|
|
values of the rate parameter lambda:
|
|
|
|
[graph exponential_pdf]
|
|
|
|
[h4 Member Functions]
|
|
|
|
exponential_distribution(RealType lambda = 1);
|
|
|
|
Constructs an
|
|
[@http://en.wikipedia.org/wiki/Exponential_distribution Exponential distribution]
|
|
with parameter /lambda/.
|
|
Lambda is defined as the reciprocal of the scale parameter.
|
|
|
|
Requires lambda > 0, otherwise calls __domain_error.
|
|
|
|
RealType lambda()const;
|
|
|
|
Accessor function returns the lambda parameter of the 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 \[0, +[infin]\].
|
|
|
|
[h4 Accuracy]
|
|
|
|
The exponential distribution is implemented in terms of the
|
|
standard library functions `exp`, `log`, `log1p` and `expm1`
|
|
and as such should have very low error rates.
|
|
|
|
[h4 Implementation]
|
|
|
|
In the following table [lambda] is the parameter lambda of the distribution,
|
|
/x/ is the random variate, /p/ is the probability and /q = 1-p/.
|
|
|
|
[table
|
|
[[Function][Implementation Notes]]
|
|
[[pdf][Using the relation: pdf = [lambda] * exp(-[lambda] * x) ]]
|
|
[[cdf][Using the relation: p = 1 - exp(-x * [lambda]) = -expm1(-x * [lambda]) ]]
|
|
[[cdf complement][Using the relation: q = exp(-x * [lambda]) ]]
|
|
[[quantile][Using the relation: x = -log(1-p) / [lambda] = -log1p(-p) / [lambda]]]
|
|
[[quantile from the complement][Using the relation: x = -log(q) / [lambda]]]
|
|
[[mean][1/[lambda]]]
|
|
[[standard deviation][1/[lambda]]]
|
|
[[mode][0]]
|
|
[[skewness][2]]
|
|
[[kurtosis][9]]
|
|
[[kurtosis excess][6]]
|
|
]
|
|
|
|
[h4 references]
|
|
|
|
* [@http://mathworld.wolfram.com/ExponentialDistribution.html Weisstein, Eric W. "Exponential Distribution." From MathWorld--A Wolfram Web Resource]
|
|
* [@http://documents.wolfram.com/calccenter/Functions/ListsMatrices/Statistics/ExponentialDistribution.html Wolfram Mathematica calculator]
|
|
* [@http://www.itl.nist.gov/div898/handbook/eda/section3/eda3667.htm NIST Exploratory Data Analysis]
|
|
* [@http://en.wikipedia.org/wiki/Exponential_distribution Wikipedia Exponential distribution]
|
|
|
|
(See also the reference documentation for the related __extreme_distrib.)
|
|
|
|
*
|
|
[@http://www.worldscibooks.com/mathematics/p191.html Extreme Value Distributions, Theory and Applications
|
|
Samuel Kotz & Saralees Nadarajah]
|
|
discuss the relationship of the types of extreme value distributions.
|
|
|
|
[endsect][/section:exp_dist Exponential]
|
|
|
|
[/ exponential.qbk
|
|
Copyright 2006 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).
|
|
]
|
|
|