---
name: "std::tr1::gamma_distribution"
section: "3cxx"
platform: "linux"
package: "libstdc++6-4.4-doc"
version: "4.4.5-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/std::tr1::gamma_distribution/3cxx"
---

# std::tr1::gamma\_distribution(3cxx)

A gamma continuous distribution for random numbers.

## NAME

std::tr1::gamma\_distribution -

A gamma continuous distribution for random numbers.

## SYNOPSIS

### Public Types

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

### Public Member Functions

\_RealType **alpha** () const \
 **gamma\_distribution** (const result\_type &\_\_alpha\_val=result\_type(1))\
 template\<class \_UniformRandomNumberGenerator \> result\_type **operator()** (\_UniformRandomNumberGenerator &\_\_urng)\
 void **reset** ()\

### Friends

template\<typename \_RealType1 , typename \_CharT , typename \_Traits \> **std::basic\_ostream**\< \_CharT, \_Traits \> & **operator\<\<** (**std::basic\_ostream**\< \_CharT, \_Traits \> &\_\_os, const **gamma\_distribution**\< \_RealType1 \> &\_\_x)\
 template\<typename \_CharT , typename \_Traits \> **std::basic\_istream**\< \_CharT, \_Traits \> & **operator\>\>** (**std::basic\_istream**\< \_CharT, \_Traits \> &\_\_is, **gamma\_distribution** &\_\_x)\

## Detailed Description

### template\<typename \_RealType = double\> class std::tr1::gamma\_distribution\< \_RealType \>

A gamma continuous distribution for random numbers.

The formula for the gamma probability mass function is $ p(x) = ac{1}{Gamma( lpha)} x^{ lpha - 1} e^{-x} $.

Definition at line 2320 of file tr1\_impl/random.

## Constructor & Destructor Documentation

### template\<typename \_RealType = double\> std::tr1::gamma\_distribution\< \_RealType \>::gamma\_distribution (const result\_type & \_\_alpha\_val = `result_type(1)`)` [inline, explicit]` Constructs a gamma distribution with parameters $ lpha $.

Definition at line 2332 of file tr1\_impl/random.

## Member Function Documentation

### template\<typename \_RealType = double\> \_RealType std::tr1::gamma\_distribution\< \_RealType \>::alpha () const` [inline]` Gets the $ lpha $ of the distribution.

Definition at line 2343 of file tr1\_impl/random.

### template\<typename \_RealType \> template\<class \_UniformRandomNumberGenerator \> gamma\_distribution\< \_RealType \>::result\_type std::tr1::gamma\_distribution\< \_RealType \>::operator() (\_UniformRandomNumberGenerator & \_\_urng) Cheng's rejection algorithm GB for alpha \>= 1 and a modification of Vaduva's rejection from Weibull algorithm due to Devroye for alpha \< 1.

References: Cheng, R. C. 'The Generation of Gamma Random Variables with Non-integral\
  Shape Parameter.' Applied Statistics, 26, 71-75, 1977.

Vaduva, I. 'Computer Generation of Gamma Gandom Variables by Rejection\
  and Composition Procedures.' Math. Operationsforschung and Statistik, Series in Statistics, 8, 545-576, 1977.

Devroye, L. 'Non-Uniform Random Variates Generation.' Springer-Verlag, New York, 1986, Ch. IX, Sect. 3.4 (+ Errata!).

Definition at line 1501 of file random.tcc.

References std::exp(), std::log(), and std::pow().

### template\<typename \_RealType = double\> void std::tr1::gamma\_distribution\< \_RealType \>::reset ()` [inline]` Resets the distribution.

Definition at line 2350 of file tr1\_impl/random.

## Friends And Related Function 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 gamma\_distribution\< \_RealType1 \> & \_\_x)` [friend]` Inserts a gamma\_distribution random number distribution `__x` into the output stream `__os`.

**Parameters:**

*\_\_os* An output stream. \
 *\_\_x* A gamma\_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 \_CharT , typename \_Traits \> std::basic\_istream\<\_CharT, \_Traits\>& operator\>\> (std::basic\_istream\< \_CharT, \_Traits \> & \_\_is, gamma\_distribution\< \_RealType \> & \_\_x)` [friend]` Extracts a gamma\_distribution random number distribution `__x` from the input stream `__is`.

**Parameters:**

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

**Returns:**

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

Definition at line 2382 of file tr1\_impl/random.

## Author

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