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- [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).
- ]
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