---
name: "std::normal_distribution"
section: "3cxx"
platform: "linux"
package: "libstdc++-12-doc"
version: "12.4.0-5"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/std::normal_distribution/3cxx"
---

# std::normal\_distribution(3cxx)

A normal continuous distribution for random numbers.

## NAME

std::normal\_distribution\< \_RealType \> - A normal continuous distribution for random numbers.

## SYNOPSIS

`#include <random>`

### Classes

struct **param\_type**\

### Public Types

**typedef** \_RealType **result\_type**\

### Public Member Functions

**normal\_distribution** (const **param\_type** &\_\_p)\
 **normal\_distribution** (**result\_type** **\_\_mean**, **result\_type** **\_\_stddev**=**result\_type**(1))\
 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.  \_RealType **mean** () const\
 Returns the mean of the distribution.  **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.  \_RealType **stddev** () const\
 Returns the standard deviation of the distribution.

### Friends

template\<**typename** **\_RealType1** , **typename** \_CharT , **typename** \_Traits \> **std::basic\_ostream**\< \_CharT, \_Traits \> & **operator\<\<** (**std::basic\_ostream**\< \_CharT, \_Traits \> &**\_\_os**, const **std::normal\_distribution**\< **\_RealType1** \> &\_\_x)\
 Inserts a normal\_distribution random number distribution `__x` into the output stream `__os`.  template\<**typename** **\_RealType1** \> bool **operator==** (const **std::normal\_distribution**\< **\_RealType1** \> &**\_\_d1**, const **std::normal\_distribution**\< **\_RealType1** \> &**\_\_d2**)\
 Return true if two normal distributions have the same parameters and the sequences that would be generated are equal.  template\<**typename** **\_RealType1** , **typename** \_CharT , **typename** \_Traits \> **std::basic\_istream**\< \_CharT, \_Traits \> & **operator\>\>** (**std::basic\_istream**\< \_CharT, \_Traits \> &**\_\_is**, **std::normal\_distribution**\< **\_RealType1** \> &\_\_x)\
 Extracts a normal\_distribution random number distribution `__x` from the input stream `__is`.

## Detailed Description

### template\<typename \_RealType = double\>

class std::normal\_distribution\< \_RealType \>"A normal continuous distribution for random numbers.

The formula for the normal probability density function is  \
     p(x\|,igma) = ac{1}{igma qrt{2 i}}\
            e^{- ac{{x - }^ {2}}{2 igma ^ {2}} }  \]

## Member Typedef Documentation

### template\<typename \_RealType = double\> typedef \_RealType std::normal\_distribution\< \_RealType \>::result\_type

The type of the range of the distribution.

## Constructor & Destructor Documentation

### template\<typename \_RealType = double\> std::normal\_distribution\< \_RealType \>::normal\_distribution (result\_type \_\_mean, result\_type \_\_stddev = result\_type`(1)`)` [inline]`, ` [explicit]`

Constructs a normal distribution with parameters $mean$ and standard deviation.

## Member Function Documentation

### template\<typename \_RealType = double\> result\_type std::normal\_distribution\< \_RealType \>::max () const` [inline]`

Returns the least upper bound value of the distribution.

References **std::numeric\_limits\< \_Tp \>::max()**.

### template\<typename \_RealType = double\> \_RealType std::normal\_distribution\< \_RealType \>::mean () const` [inline]`

Returns the mean of the distribution.

### template\<typename \_RealType = double\> result\_type std::normal\_distribution\< \_RealType \>::min () const` [inline]`

Returns the greatest lower bound value of the distribution.

References **std::numeric\_limits\< \_Tp \>::lowest()**.

### template\<typename \_RealType = double\> template\<typename \_UniformRandomNumberGenerator \> result\_type std::normal\_distribution\< \_RealType \>::operator() (\_UniformRandomNumberGenerator & \_\_urng)` [inline]`

Generating functions.

References **std::normal\_distribution\< \_RealType \>::operator()()**.

Referenced by **std::normal\_distribution\< \_RealType \>::operator()()**.

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

Polar method due to Marsaglia.

Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag, New York, 1986, Ch. V, Sect. 4.4.

References **std::log()**, and **std::sqrt()**.

### template\<typename \_RealType = double\> param\_type std::normal\_distribution\< \_RealType \>::param () const` [inline]`

Returns the parameter set of the distribution.

### template\<typename \_RealType = double\> void std::normal\_distribution\< \_RealType \>::param (const param\_type & \_\_param)` [inline]`

Sets the parameter set of the distribution.

**Parameters**

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

### template\<typename \_RealType = double\> void std::normal\_distribution\< \_RealType \>::reset ()` [inline]`

Resets the distribution state.

Referenced by **std::lognormal\_distribution\< \_RealType \>::reset()**, **std::gamma\_distribution\< \_RealType \>::reset()**, **std::student\_t\_distribution\< \_RealType \>::reset()**, **std::binomial\_distribution\< \_IntType \>::reset()**, and **std::poisson\_distribution\< \_IntType \>::reset()**.

### template\<typename \_RealType = double\> \_RealType std::normal\_distribution\< \_RealType \>::stddev () const` [inline]`

Returns the standard deviation of the distribution.

## Friends And Related Symbol Documentation

### template\<typename \_RealType = double\> template\<typename \_RealType1 , typename \_CharT , typename \_Traits \> std::basic\_ostream\< \_CharT, \_Traits \> & operator\<\< (std::basic\_ostream\< \_CharT, \_Traits \> & \_\_os, const std::normal\_distribution\< \_RealType1 \> & \_\_x)` [friend]`

Inserts a normal\_distribution random number distribution `__x` into the output stream `__os`.

**Parameters**

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

**Returns**

The output stream with the state of `__x` inserted or in an error state.

### template\<typename \_RealType = double\> template\<typename \_RealType1 \> bool operator== (const std::normal\_distribution\< \_RealType1 \> & \_\_d1, const std::normal\_distribution\< \_RealType1 \> & \_\_d2)` [friend]`

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

### template\<typename \_RealType = double\> template\<typename \_RealType1 , typename \_CharT , typename \_Traits \> std::basic\_istream\< \_CharT, \_Traits \> & operator\>\> (std::basic\_istream\< \_CharT, \_Traits \> & \_\_is, std::normal\_distribution\< \_RealType1 \> & \_\_x)` [friend]`

Extracts a normal\_distribution random number distribution `__x` from the input stream `__is`.

**Parameters**

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

**Returns**

The input stream with `__x` extracted or in an error state.

## Author

Generated automatically by Doxygen for libstdc++ from the source code.