DEXPPF Subroutine

public subroutine DEXPPF(P, Ppf)

NAME

dexppf(3f) - [M_datapac:PERCENT_POINT] compute the double exponential
percent point function

SYNOPSIS

   SUBROUTINE DEXPPF(P,Ppf)

    REAL(kind=wp),intent(in)  :: P
    REAL(kind=wp),intent(out) :: Ppf

DESCRIPTION

DEXPPF(3f) computes the percent point function value for the double
exponential (laplace) distribution with mean = 0 and standard deviation
= sqrt(2).

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

   f(x) = 0.5*exp(-abs(x)).

Note that the percent point function of a distribution is identically
the same as the inverse cumulative distribution function of the
distribution.

INPUT ARGUMENTS

P      The value (between 0.0 and 1.0, EXCLUSIVELY) at which the
       percent point function is to be evaluated.

OUTPUT ARGUMENTS

PPF    The percent point function value.

EXAMPLES

Sample program:

program demo_dexppf
use M_datapac, only : dexppf
implicit none
! call dexppf(x,y)
end program demo_dexppf

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

  • Filliben, Simple and Robust Linear Estimation of the Location Parameter of a Symmetric Distribution (Unpublished PH.D. Dissertation, Princeton University), 1969, pages 21-44, 229-231.
  • Filliben, ‘The Percent Point Function’, (Unpublished Manuscript), 1970, pages 28-31.
  • Johnson and Kotz, Continuous Univariate Distributions–2, 1970, pages 22-36.

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in) :: P
real(kind=wp), intent(out) :: Ppf

Source Code

SUBROUTINE DEXPPF(P,Ppf)
REAL(kind=wp),intent(in)  :: P
REAL(kind=wp),intent(out) :: Ppf
!
!     CHECK THE INPUT ARGUMENTS FOR ERRORS
!
      IF ( P<=0.0_wp .OR. P>=1.0_wp ) THEN
         WRITE (G_IO,99001)
         99001 FORMAT (' ***** FATAL ERROR--THE FIRST  INPUT ARGUMENT TO DEXPPF(3f) IS OUTSIDE THE ALLOWABLE (0,1) INTERVAL *****')
         WRITE (G_IO,99002) P
         99002 FORMAT (' ','***** THE VALUE OF THE ARGUMENT IS ',E15.8, ' *****')
         RETURN
      ELSE
         IF ( P<=0.5_wp ) Ppf = LOG(2.0_wp*P)
         IF ( P>0.5_wp ) Ppf = -LOG(2.0_wp*(1.0_wp-P))
      ENDIF

END SUBROUTINE DEXPPF