# Gumbel

Generates Gumbel distributed random values.

## Syntax

Fortran:

status = vsrnggumbel( method, stream, n, r, a, beta )

status = vdrnggumbel( method, stream, n, r, a, beta )

C:

status = vsRngGumbel( method, stream, n, r, a, beta );

status = vdRngGumbel( method, stream, n, r, a, beta );

## Description

This function generates Gumbel distributed random numbers with displacement a and scalefactor β, where a, β∈R ; β > 0.

The probability density function is given by:

The cumulative distribution function is as follows:

## Input Parameters

Name | Type | Description
--- | --- | ---
method | FORTRAN: INTEGER, INTENT(IN) C: int | Generation method. The specific values are as follows: `VSL_METHOD_SGUMBEL_ICDF` `VSL_METHOD_DGUMBEL_ICDF` Inverse cumulative distribution function method
stream | FORTRAN: TYPE (VSL_STREAM_STATE), INTENT(IN) C: VSLStreamStatePtr | FORTRAN: Descriptor of the stream state structure C: Pointer to the stream state structure
n | FORTRAN: INTEGER, INTENT(IN) C: int | Number of random values to be generated
a | FORTRAN: REAL, INTENT(IN) for vsrnggumbel DOUBLE PRECISION, INTENT(IN) for vdrnggumbel C: float for vsRngGumbel double for vdRngGumbel | Displacement a.
beta | FORTRAN: REAL, INTENT(IN) for vsrnggumbel DOUBLE PRECISION, INTENT(IN) for vdrnggumbel C: float for vsRngGumbel double for vdRngGumbel | Scalefactor β.

## Output Parameters

Name | Type | Description
--- | --- | ---
r | FORTRAN: REAL, INTENT(OUT) for vsrnggumbel DOUBLE PRECISION, INTENT(OUT) for vdrnggumbel C: float* for vsRngGumbel double* for vdRngGumbel | Vector of n random numbers with Gumbel distribution

## Return Values

VSL_ERROR_OK, VSL_STATUS_OK
  Indicates no error, execution is successful.
VSL_ERROR_NULL_PTR
  stream is a NULL pointer.
VSL_ERROR_BAD_STREAM

  stream is not a valid random stream.

VSL_ERROR_BAD_UPDATE

  Callback function for an abstract BRNG returns an invalid number of updated entries in a buffer, that is, `< 0` or `> nmax`.

VSL_ERROR_NO_NUMBERS

  Callback function for an abstract BRNG returns 0 as the number of updated entries in a buffer.

Parent topic: Continuous Distributions