This function evaluates the extreme value cumulative distribution function.

Function Return Value

EXVDF — Function value, the probability that an extreme value random variable takes a value less than or equal to X.   (Output)

Required Arguments

X — Argument for which the extreme value cumulative distribution function is to be evaluated.   (Input)

AMU — Location parameter of the extreme value probability distribution function.   (Input)

BETA — Scale parameter of the extreme value probability distribution function.   (Input)

FORTRAN 90 Interface

Generic:                              EXVDF (X, AMU, BETA)

Specific:                             The specific interface names are S_EXVDF and D_EXVDF.

FORTRAN 77 Interface

Single:                                EXVDF (X, AMU, BETA)

Double:                              The double precision name is DEXVDF.

Description

The function EXVDF evaluates the extreme value cumulative distribution function, defined as

 

 

The extreme value distribution is also known as the Gumbel minimum distribution.

Example

In this example, we evaluate the probability function at X = 1.0, AMU = 0.0, BETA = 1.0.

 

      USE UMACH_INT
      USE EXVDF_INT
      IMPLICIT NONE

      INTEGER NOUT

      REAL X, AMU, B, PR

      CALL UMACH(2, NOUT)

      X = 1.0

      AMU = 0.0

      B = 1.0

      PR = EXVDF(X, AMU, B)

      WRITE (NOUT, 99999) X, AMU, B, PR

99999 FORMAT (' EXVDF(', F6.2, ', ', F4.2, ', ', F4.2, ') = ', F6.4)

      END

Output

 

EXVDF(  1.00, 0.00, 1.00) = 0.9340

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