DEXSF Subroutine

public subroutine DEXSF(P, Sf)

NAME

dexsf(3f) - [M_datapac:SPARSITY] compute the double exponential
sparsity function

SYNOPSIS

   SUBROUTINE DEXSF(P,Sf)

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

DESCRIPTION

DEXSF(3f) computes the sparsity 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 sparsity function of a distribution is the derivative
of the percent point function, and also is the reciprocal of the
probability density function (but in units of P rather than X).

INPUT ARGUMENTS

P      The value (between 0.0 and 1.0 exclusively) at which the
       sparsity function is to be evaluated.

OUTPUT ARGUMENTS

SF     The sparsity function value.

EXAMPLES

Sample program:

program demo_dexsf
use M_datapac, only : dexsf
implicit none
! call dexsf(x,y)
end program demo_dexsf

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  • Filliben, Simple and Robust Linear Estimation of the Location Parameter of a Symmetric Distribution (Unpublished PH.D. Dissertation, Princeton University), 1969, pages 21-44, 229-231.
  • Filliben, ‘The Percent Point Function’, (UNpublished Manuscript), 1970, pages 28-31.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) :: Sf

Source Code

SUBROUTINE DEXSF(P,Sf)
REAL(kind=wp),intent(in) :: P
REAL(kind=wp),intent(out) :: Sf
!
!     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 DEXSF(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 ) Sf = 1.0_wp/P
      IF ( P>0.5_wp ) Sf = 1.0_wp/(1.0_wp-P)
   ENDIF
!
END SUBROUTINE DEXSF