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Difference between revisions of "cpp/numeric/random/exponential distribution"

From cppreference.com
< cpp‎ | numeric‎ | random
m (reqs)
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{{cpp/title|exponential_distribution}}
 
{{cpp/title|exponential_distribution}}
 
{{cpp/numeric/random/exponential_distribution/navbar}}
 
{{cpp/numeric/random/exponential_distribution/navbar}}
−
{{ddcl | header=random | since=c++11 | 1=
+
{{ddcl|header=random|since=c++11|1=
 
template< class RealType = double >
 
template< class RealType = double >
 
class exponential_distribution;
 
class exponential_distribution;
 
}}
 
}}
  
−
Produces random non-negative floating-point values {{math|x}}, distributed according to probability density function:
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Produces random non-negative floating-point values {{mathjax-or|\(\small x\)|x}}, distributed according to probability density function:
  
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:{{math|P(x{{!}}λ) {{=}} λe{{su|p=-λx}}}}
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:{{mathjax-or|1=\(\small P(x{{!}}\lambda) = \lambda e^{-\lambda x}\)|2=P(x{{!}}λ) = λe{{su|p=-λx}}}}
  
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The value obtained is the time/distance until the next random event if random events occur at constant rate {{math|λ}} per unit of time/distance. For example, this distribution describes the time between the clicks of a Geiger counter or the distance between point mutations in a DNA strand.
+
The value obtained is the time/distance until the next random event if random events occur at constant rate {{mathjax-or|\(\small\lambda\)|λ}} per unit of time/distance. For example, this distribution describes the time between the clicks of a Geiger counter or the distance between point mutations in a DNA strand.
  
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This is the continuous counterpart of {{lc|std::geometric_distribution}}
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This is the continuous counterpart of {{lc|std::geometric_distribution}}.
  
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{{tt|std::exponential_distribution}} satisfies {{concept|RandomNumberDistribution}}
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{{tt|std::exponential_distribution}} satisfies {{named req|RandomNumberDistribution}}.
  
 
===Template parameters===
 
===Template parameters===
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===Member types===
 
===Member types===
 
{{dsc begin}}
 
{{dsc begin}}
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{{dsc hitem | Member type | Definition}}
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{{dsc hitem|Member type|Definition}}
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{{dsc | {{tt|result_type}} | {{c|RealType}}}}
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{{dsc|{{tt|result_type}} {{mark c++11}}|{{co|RealType}}}}
 
{{cpp/numeric/random/param_type}}
 
{{cpp/numeric/random/param_type}}
 
{{dsc end}}
 
{{dsc end}}
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===Member functions===
 
===Member functions===
 
{{dsc begin}}
 
{{dsc begin}}
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{{dsc inc | cpp/numeric/random/distribution/dsc constructor | exponential_distribution}}
+
{{dsc inc|cpp/numeric/random/distribution/dsc constructor|exponential_distribution}}
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{{dsc inc | cpp/numeric/random/distribution/dsc reset | exponential_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc reset|exponential_distribution}}
  
−
{{dsc h2 | Generation}}
+
{{dsc h2|Generation}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc operator() | exponential_distribution}}
+
{{dsc inc|cpp/numeric/random/distribution/dsc operator()|exponential_distribution}}
  
−
{{dsc h2 | Characteristics}}
+
{{dsc h2|Characteristics}}
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{{dsc inc | cpp/numeric/random/exponential_distribution/dsc lambda}}
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{{dsc inc|cpp/numeric/random/exponential_distribution/dsc lambda}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc param | exponential_distribution}}
+
{{dsc inc|cpp/numeric/random/distribution/dsc param|exponential_distribution}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc min | exponential_distribution}}
+
{{dsc inc|cpp/numeric/random/distribution/dsc min|exponential_distribution}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc max | exponential_distribution}}
+
{{dsc inc|cpp/numeric/random/distribution/dsc max|exponential_distribution}}
 
{{dsc end}}
 
{{dsc end}}
  
 
===Non-member functions===
 
===Non-member functions===
 
{{dsc begin}}
 
{{dsc begin}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc operator_cmp | exponential_distribution }}
+
{{dsc inc|cpp/numeric/random/distribution/dsc operator_cmp|exponential_distribution}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc operator_ltltgtgt | exponential_distribution}}
+
{{dsc inc|cpp/numeric/random/distribution/dsc operator_ltltgtgt|exponential_distribution}}
 
{{dsc end}}
 
{{dsc end}}
 +
 +
===Notes===
 +
Some implementations may occasionally return infinity if {{tt|RealType}} is {{c|float}}. This is {{lwg|2524}}.
  
 
===Example===
 
===Example===
 
{{example
 
{{example
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| code=
+
|code=
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#include <iostream>
+
 
#include <iomanip>
 
#include <iomanip>
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#include <string>
+
#include <iostream>
 
#include <map>
 
#include <map>
 
#include <random>
 
#include <random>
 +
#include <string>
 +
 
int main()
 
int main()
 
{
 
{
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     std::map<int, int> hist;
 
     std::map<int, int> hist;
−
     for(int n=0; n<10000; ++n) {
+
     for (int n = 0; n != 10000; ++n)
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         ++hist[2*d(gen)];
+
         ++hist[2 * d(gen)];
−
    }
+
 
−
     for(auto p : hist) {
+
     for (auto const& [x, y] : hist)
−
         std::cout << std::fixed << std::setprecision(1)  
+
         std::cout << std::fixed << std::setprecision(1)
−
                   << p.first/2.0 << '-' << (p.first+1)/2.0 <<
+
                   << x / 2.0 << '-' << (x + 1) / 2.0 << ' '
−
                ' ' << std::string(p.second/200, '*') << '\n';
+
                  << std::string(y / 200, '*') << '\n';
−
    }
+
 
}
 
}
−
| p=true
+
|p=true
−
| output=
+
|output=
 
0.0-0.5 *******************
 
0.0-0.5 *******************
 
0.5-1.0 ***********
 
0.5-1.0 ***********
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2.0-2.5 **
 
2.0-2.5 **
 
2.5-3.0 *
 
2.5-3.0 *
−
3.0-3.5  
+
3.0-3.5
−
3.5-4.0  
+
3.5-4.0
 
}}
 
}}
  
 
===External links===
 
===External links===
−
[http://mathworld.wolfram.com/ExponentialDistribution.html Weisstein, Eric W. "Exponential Distribution."] From MathWorld--A Wolfram Web Resource.
+
{{eli|[https://mathworld.wolfram.com/ExponentialDistribution.html Weisstein, Eric W. "Exponential Distribution."] From MathWorld &mdash; A Wolfram Web Resource.}}
  
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[[de:cpp/numeric/random/exponential distribution]]
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{{langlinks|de|es|fr|it|ja|pt|ru|zh}}
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[[es:cpp/numeric/random/exponential distribution]]
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[[fr:cpp/numeric/random/exponential distribution]]
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[[it:cpp/numeric/random/exponential distribution]]
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[[ja:cpp/numeric/random/exponential distribution]]
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[[pt:cpp/numeric/random/exponential distribution]]
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[[ru:cpp/numeric/random/exponential distribution]]
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[[zh:cpp/numeric/random/exponential distribution]]
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Latest revision as of 10:29, 17 October 2023

 
C++
 
Numerics library
Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
Factor operations
(C++17)
(C++17)
Interpolations
(C++20)
(C++20)
Saturation arithmetic
(C++26)
(C++26)
(C++26)
(C++26)
(C++26)

Generic numeric operations
Bit operations
(C++20)    
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++23)
(C++20)
 
Pseudo-random number generation
 
std::exponential_distribution
 
Defined in header <random>
template< class RealType = double >
class exponential_distribution;
 (since C++11)

Produces random non-negative floating-point values x, distributed according to probability density function:

P(x|λ) = λe-λx

The value obtained is the time/distance until the next random event if random events occur at constant rate λ per unit of time/distance. For example, this distribution describes the time between the clicks of a Geiger counter or the distance between point mutations in a DNA strand.

This is the continuous counterpart of std::geometric_distribution.

std::exponential_distribution satisfies RandomNumberDistribution.

Contents

[edit] Template parameters

RealType - The result type generated by the generator. The effect is undefined if this is not one of float, double, or long double.

[edit] Member types

Member type Definition
result_type (C++11) RealType
param_type (C++11) the type of the parameter set, see RandomNumberDistribution.

[edit] Member functions

(C++11)
 constructs new distribution
(public member function) [edit]
(C++11)
 resets the internal state of the distribution
(public member function) [edit]
Generation
(C++11)
 generates the next random number in the distribution
(public member function) [edit]
Characteristics
(C++11)
 returns the lambda distribution parameter (rate of events)
(public member function) [edit]
(C++11)
 gets or sets the distribution parameter object
(public member function) [edit]
(C++11)
 returns the minimum potentially generated value
(public member function) [edit]
(C++11)
 returns the maximum potentially generated value
(public member function) [edit]

[edit] Non-member functions

(C++11)(C++11)(removed in C++20)
 compares two distribution objects
(function) [edit]
(C++11)
 performs stream input and output on pseudo-random number distribution
(function template) [edit]

[edit] Notes

Some implementations may occasionally return infinity if RealType is float. This is LWG issue 2524.

[edit] Example

Run this code
#include <iomanip>
#include <iostream>
#include <map>
#include <random>
#include <string>
 
int main()
{
    std::random_device rd;
    std::mt19937 gen(rd());
 
    // if particles decay once per second on average,
    // how much time, in seconds, until the next one?
    std::exponential_distribution<> d(1);
 
    std::map<int, int> hist;
    for (int n = 0; n != 10000; ++n)
        ++hist[2 * d(gen)];
 
    for (auto const& [x, y] : hist)
        std::cout << std::fixed << std::setprecision(1)
                  << x / 2.0 << '-' << (x + 1) / 2.0 << ' '
                  << std::string(y / 200, '*') << '\n';
}

Possible output: 

0.0-0.5 *******************
0.5-1.0 ***********
1.0-1.5 *******
1.5-2.0 ****
2.0-2.5 **
2.5-3.0 *
3.0-3.5
3.5-4.0

[edit] External links

Weisstein, Eric W. "Exponential Distribution." From MathWorld — A Wolfram Web Resource.
Retrieved from "https://en.cppreference.com/mwiki/index.php?title=cpp/numeric/random/exponential_distribution&oldid=160836"