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

From cppreference.com
< cpp‎ | numeric‎ | random
m (list allowed types for IntType)
m (., headers sorted)
 
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{{cpp/title|poisson_distribution}}
 
{{cpp/title|poisson_distribution}}
 
{{cpp/numeric/random/poisson_distribution/navbar}}
 
{{cpp/numeric/random/poisson_distribution/navbar}}
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{{ddcl | header=random | since=c++11 | 1=
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{{ddcl|header=random|since=c++11|1=
 
template< class IntType = int >
 
template< class IntType = int >
 
class poisson_distribution;
 
class poisson_distribution;
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Produces random non-negative integer values {{math|i}}, distributed according to discrete probability function:
 
Produces random non-negative integer values {{math|i}}, distributed according to discrete probability function:
  
−
:{{math|P(i{{!}}μ) {{=}} {{mfrac|e{{su|p=-μ}}·μ{{su|p=i}}|i!}}}}
+
:{{mathjax-or|1=\(P(i {{!}} \mu) = \frac{e^{-\mu}\mu^i}{i!}\)|2=P(i{{!}}μ) = {{mfrac|e{{su|p=-μ}}·μ{{su|p=i}}|i!}}}}
  
 
The value obtained is the probability of exactly {{math|i}} occurrences of a random event if the expected, ''mean'' number of its occurrence under the same conditions (on the same time/space interval) is {{math|μ}}.
 
The value obtained is the probability of exactly {{math|i}} occurrences of a random event if the expected, ''mean'' number of its occurrence under the same conditions (on the same time/space interval) is {{math|μ}}.
 +
 +
{{tt|std::poisson_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|IntType}}}}
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{{dsc|{{tt|result_type}} {{mark c++11}}|{{tt|IntType}}}}
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{{dsc | {{tt|param_type}} | the type of the parameter set, unspecified}}
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{{cpp/numeric/random/param_type}}
 
{{dsc end}}
 
{{dsc end}}
  
 
===Member functions===
 
===Member functions===
 
{{dsc begin}}
 
{{dsc begin}}
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{{dsc inc | cpp/numeric/random/distribution/dsc constructor | poisson_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc constructor|poisson_distribution}}
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{{dsc inc | cpp/numeric/random/distribution/dsc reset | poisson_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc reset|poisson_distribution}}
  
−
{{dsc h2 | Generation}}
+
{{dsc h2|Generation}}
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{{dsc inc | cpp/numeric/random/distribution/dsc operator() | poisson_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc operator()|poisson_distribution}}
  
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{{dsc h2 | Characteristics}}
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{{dsc h2|Characteristics}}
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{{dsc inc | cpp/numeric/random/poisson_distribution/dsc mean}}
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{{dsc inc|cpp/numeric/random/poisson_distribution/dsc mean}}
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{{dsc inc | cpp/numeric/random/distribution/dsc param | poisson_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc param|poisson_distribution}}
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{{dsc inc | cpp/numeric/random/distribution/dsc min | poisson_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc min|poisson_distribution}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc max | poisson_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc max|poisson_distribution}}
 
{{dsc end}}
 
{{dsc end}}
  
 
===Non-member functions===
 
===Non-member functions===
 
{{dsc begin}}
 
{{dsc begin}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc operator_cmp | poisson_distribution }}
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{{dsc inc|cpp/numeric/random/distribution/dsc operator_cmp|poisson_distribution}}
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{{dsc inc | cpp/numeric/random/distribution/dsc operator_ltltgtgt | poisson_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc operator_ltltgtgt|poisson_distribution}}
 
{{dsc end}}
 
{{dsc end}}
  
 
===Example===
 
===Example===
 
{{example
 
{{example
−
| code=
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|code=
−
#include <iostream>
+
 
#include <iomanip>
 
#include <iomanip>
−
#include <string>
+
#include <iostream>
 
#include <map>
 
#include <map>
 
#include <random>
 
#include <random>
 +
#include <string>
 +
 
int main()
 
int main()
 
{
 
{
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     std::mt19937 gen(rd());
 
     std::mt19937 gen(rd());
  
−
     // if an event occurs 4 times a minute on average
+
     // If an event occurs 4 times a minute on average, how
−
     // how often is it that it occurs n times in one minute?
+
     // often is it that it occurs n times in one minute?
 
     std::poisson_distribution<> d(4);
 
     std::poisson_distribution<> d(4);
  
 
     std::map<int, int> hist;
 
     std::map<int, int> hist;
−
     for(int n=0; n<10000; ++n) {
+
     for (int n = 0; n != 10000; ++n)
 
         ++hist[d(gen)];
 
         ++hist[d(gen)];
−
    }
+
 
−
     for(auto p : hist) {
+
     for (auto [x, y] : hist)
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         std::cout << p.first <<
+
         std::cout << std::hex << x << ' '
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                ' ' << std::string(p.second/100, '*') << '\n';
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                  << std::string(y / 100, '*') << '\n';
−
    }
+
 
}
 
}
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| output=
+
|p=true
 +
|output=
 
0 *
 
0 *
 
1 *******
 
1 *******
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8 **
 
8 **
 
9 *
 
9 *
−
10
+
a
−
11
+
b
−
12
+
c
−
13
+
d
 
}}
 
}}
  
 
===External links===
 
===External links===
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[http://mathworld.wolfram.com/PoissonDistribution.html Weisstein, Eric W. "Poisson Distribution."] From MathWorld--A Wolfram Web Resource.
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{{elink begin}}
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{{elink|[https://mathworld.wolfram.com/PoissonDistribution.html Weisstein, Eric W. "Poisson Distribution."] From MathWorld &mdash; A Wolfram Web Resource.}}
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{{elink end}}
  
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Latest revision as of 08:46, 5 May 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::poisson_distribution
 
Defined in header <random>
template< class IntType = int >
class poisson_distribution;
 (since C++11)

Produces random non-negative integer values i, distributed according to discrete probability function:

P(i|μ) =
e-μ·μi
i!

The value obtained is the probability of exactly i occurrences of a random event if the expected, mean number of its occurrence under the same conditions (on the same time/space interval) is μ.

std::poisson_distribution satisfies RandomNumberDistribution.

Contents

[edit] Template parameters

IntType - The result type generated by the generator. The effect is undefined if this is not one of short, int, long, long long, unsigned short, unsigned int, unsigned long, or unsigned long long.

[edit] Member types

Member type Definition
result_type (C++11) IntType
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 mean distribution parameter (mean number of occurrences of the event)
(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] 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 an event occurs 4 times a minute on average, how
    // often is it that it occurs n times in one minute?
    std::poisson_distribution<> d(4);
 
    std::map<int, int> hist;
    for (int n = 0; n != 10000; ++n)
        ++hist[d(gen)];
 
    for (auto [x, y] : hist)
        std::cout << std::hex << x << ' '
                  << std::string(y / 100, '*') << '\n';
}

Possible output: 

0 *
1 *******
2 **************
3 *******************
4 *******************
5 ***************
6 **********
7 *****
8 **
9 *
a
b
c
d

[edit] External links

  Weisstein, Eric W. "Poisson Distribution." From MathWorld — A Wolfram Web Resource.
Retrieved from "https://en.cppreference.com/mwiki/index.php?title=cpp/numeric/random/poisson_distribution&oldid=151389"