EV1CDF Subroutine

public subroutine EV1CDF(X, Cdf)

NAME

ev1cdf(3f) - [M_datapac:CUMULATIVE_DISTRIBUTION] compute the extreme value type 1
(Gumbel) cumulative distribution function

SYNOPSIS

   SUBROUTINE EV1CDF(X,Cdf)

    REAL(kind=wp),intent(in) :: X
    REAL(kind=wp),intent(out) :: Cdf

DESCRIPTION

EV1CDF(3f) computes the cumulative distribution function value for
the extreme value type 1 distribution.

The extreme value type 1 distribution used herein has mean = Euler's
number = 0.57721566 and standard deviation = pi/sqrt(6) = 1.28254983.

This distribution is defined for all X and has the probability
density function

    f(X) = (exp(-X)) * (exp(-(exp(-X))))

INPUT ARGUMENTS

X     The value at which the cumulative distribution function is
      to be evaluated.

OUTPUT ARGUMENTS

CDF   The cumulative distribution function value.

EXAMPLES

Sample program:

program demo_ev1cdf
use M_datapac, only : ev1cdf
implicit none
! call ev1cdf(x,y)
end program demo_ev1cdf

Results:

AUTHOR

The original DATAPAC library was written by James Filliben of the
Statistical Engineering Division, National Institute of Standards
and Technology.

MAINTAINER

John Urban, 2022.05.31

LICENSE

CC0-1.0

REFERENCES

  • Johnson and Kotz, Continuous Univariate Distributions–1, 1970, pages 272-295.

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in) :: X
real(kind=wp), intent(out) :: Cdf

Source Code

SUBROUTINE EV1CDF(X,Cdf)
REAL(kind=wp),intent(in) :: X
REAL(kind=wp),intent(out) :: Cdf

!     CHECK THE INPUT ARGUMENTS FOR ERRORS. -- NO INPUT ARGUMENT ERRORS POSSIBLE FOR THIS DISTRIBUTION.

      Cdf = 1.0_wp - EXP(-(EXP(-X)))

END SUBROUTINE EV1CDF