---
name: "std::normal_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::normal_distribution"
---

# std::normal\_distribution(3)

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    \
            e^{- ac{{x - }^ {2}}{2 igma ^ {2}} } \]

**Since**

C++11

## 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.

### 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.

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

Generating functions.

Referenced by **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.

### 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

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