---
name: "std::poisson_distribution"
section: "3"
platform: "linux"
package: "gcc"
version: "16.2.1+r23+gd564253eb6c8-1"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/std::poisson_distribution"
---

# std::poisson\_distribution(3)

A discrete Poisson random number distribution.

## NAME

std::poisson\_distribution\< \_IntType \> - A discrete Poisson random number distribution.

## SYNOPSIS

\#include \<random\>

### Classes

struct **param\_type**\

### Public Types

typedef \_IntType **result\_type**\

### Public Member Functions

**poisson\_distribution** (const **param\_type** &\_\_p)\
 **poisson\_distribution** (double \_\_mean)\
 template\<typename \_ForwardIterator, typename \_UniformRandomNumberGenerator\> void **\_\_generate** (\_ForwardIterator \_\_f, \_ForwardIterator \_\_t, \_UniformRandomNumberGenerator &\_\_urng)\
 template\<typename \_ForwardIterator, typename \_UniformRandomNumberGenerator\> void **\_\_generate** (\_ForwardIterator \_\_f, \_ForwardIterator \_\_t, \_UniformRandomNumberGenerator &\_\_urng, const **param\_type** &\_\_p)\
 template\<typename \_UniformRandomNumberGenerator\> void **\_\_generate** (**result\_type** \*\_\_f, **result\_type** \*\_\_t, \_UniformRandomNumberGenerator &\_\_urng, const **param\_type** &\_\_p)\
 **result\_type** **max** () const\
 Returns the least upper bound value of the distribution.  double **mean** () const\
 Returns the distribution parameter mean.  **result\_type** **min** () const\
 Returns the greatest lower bound value of the distribution.  template\<typename \_UniformRandomNumberGenerator\> **result\_type** **operator()** (\_UniformRandomNumberGenerator &\_\_urng)\
 Generating functions.  template\<typename \_UniformRandomNumberGenerator\> **result\_type** **operator()** (\_UniformRandomNumberGenerator &\_\_urng, const **param\_type** &\_\_p)\
 **param\_type** **param** () const\
 Returns the parameter set of the distribution.  void **param** (const **param\_type** &\_\_param)\
 Sets the parameter set of the distribution.  void **reset** ()\
 Resets the distribution state.

### Friends

template\<typename \_IntType1, typename \_CharT, typename \_Traits\> **std::basic\_ostream**\< \_CharT, \_Traits \> & **operator\<\<** (**std::basic\_ostream**\< \_CharT, \_Traits \> &\_\_os, const **std::poisson\_distribution**\< \_IntType1 \> &\_\_x)\
 Inserts a poisson\_distribution random number distribution \_\_x into the output stream \_\_os.  bool **operator==** (const poisson\_distribution &\_\_d1, const poisson\_distribution &\_\_d2)\
 Return true if two Poisson distributions have the same parameters and the sequences that would be generated are equal.  template\<typename \_IntType1, typename \_CharT, typename \_Traits\> **std::basic\_istream**\< \_CharT, \_Traits \> & **operator\>\>** (**std::basic\_istream**\< \_CharT, \_Traits \> &\_\_is, **std::poisson\_distribution**\< \_IntType1 \> &\_\_x)\
 Extracts a poisson\_distribution random number distribution \_\_x from the input stream \_\_is.

## Detailed Description

### template\<typename \_IntType = int\>

class std::poisson\_distribution\< \_IntType \>"A discrete Poisson random number distribution.

The formula for the Poisson probability density function is $p(i\|) = ac{^i}{i!} e^{-}$ where $$ is the parameter of the distribution.

**Since**

C++11

## Member Typedef Documentation

### template\<typename \_IntType = int\> typedef \_IntType std::poisson\_distribution\< \_IntType \>::result\_type

The type of the range of the distribution.

## Member Function Documentation

### template\<typename \_IntType = int\> result\_type std::poisson\_distribution\< \_IntType \>::max () const \[inline\]

Returns the least upper bound value of the distribution.

### template\<typename \_IntType = int\> double std::poisson\_distribution\< \_IntType \>::mean () const \[inline\]

Returns the distribution parameter mean.

### template\<typename \_IntType = int\> result\_type std::poisson\_distribution\< \_IntType \>::min () const \[inline\]

Returns the greatest lower bound value of the distribution.

### template\<typename \_IntType = int\> template\<typename \_UniformRandomNumberGenerator\> result\_type std::poisson\_distribution\< \_IntType \>::operator() (\_UniformRandomNumberGenerator & \_\_urng) \[inline\]

Generating functions.

Referenced by **operator()()**.

### template\<typename \_IntType\> template\<typename \_UniformRandomNumberGenerator\> poisson\_distribution\< \_IntType \>::result\_type std::poisson\_distribution\< \_IntType \>::operator() (\_UniformRandomNumberGenerator & \_\_urng, const param\_type & \_\_param)

A rejection algorithm when mean \>= 12 and a simple method based upon the multiplication of uniform random variates otherwise. NB: The former is available only if \_GLIBCXX\_USE\_C99\_MATH\_FUNCS is defined.

Reference: Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag, New York, 1986, Ch. X, Sects. 3.3 & 3.4 (+ Errata!).

References **std::abs()**, **std::numeric\_limits\< \_Tp \>::epsilon()**, **std::log()**, and **std::numeric\_limits\< \_Tp \>::max()**.

### template\<typename \_IntType = int\> param\_type std::poisson\_distribution\< \_IntType \>::param () const \[inline\]

Returns the parameter set of the distribution.

### template\<typename \_IntType = int\> void std::poisson\_distribution\< \_IntType \>::param (const param\_type & \_\_param) \[inline\]

Sets the parameter set of the distribution.

**Parameters**

*\_\_param* The new parameter set of the distribution.

### template\<typename \_IntType = int\> void std::poisson\_distribution\< \_IntType \>::reset () \[inline\]

Resets the distribution state.

## Friends And Related Symbol Documentation

### template\<typename \_IntType = int\> template\<typename \_IntType1, typename \_CharT, typename \_Traits\> std::basic\_ostream\< \_CharT, \_Traits \> & operator\<\< (std::basic\_ostream\< \_CharT, \_Traits \> & \_\_os, const std::poisson\_distribution\< \_IntType1 \> & \_\_x) \[friend\]

Inserts a poisson\_distribution random number distribution \_\_x into the output stream \_\_os.

**Parameters**

*\_\_os* An output stream. \
 *\_\_x* A poisson\_distribution random number distribution.

**Returns**

The output stream with the state of \_\_x inserted or in an error state.

### template\<typename \_IntType = int\> bool operator== (const poisson\_distribution\< \_IntType \> & \_\_d1, const poisson\_distribution\< \_IntType \> & \_\_d2) \[friend\]

Return true if two Poisson distributions have the same parameters and the sequences that would be generated are equal.

### template\<typename \_IntType = int\> template\<typename \_IntType1, typename \_CharT, typename \_Traits\> std::basic\_istream\< \_CharT, \_Traits \> & operator\>\> (std::basic\_istream\< \_CharT, \_Traits \> & \_\_is, std::poisson\_distribution\< \_IntType1 \> & \_\_x) \[friend\]

Extracts a poisson\_distribution random number distribution \_\_x from the input stream \_\_is.

**Parameters**

*\_\_is* An input stream. \
 *\_\_x* A poisson\_distribution random number generator engine.

**Returns**

The input stream with \_\_x extracted or in an error state.

## Author

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