UNISF Subroutine

public subroutine UNISF(P, Sf)

NAME

unisf(3f) - [M_datapac:SPARSITY] compute the Uniform sparsity function

SYNOPSIS

   SUBROUTINE UNISF(P,Sf)

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

DESCRIPTION

UNISF(3f) computes the sparsity function value for the uniform
(rectangular) distribution on the unit interval (0,1).

This distribution has mean = 0.5 and standard deviation = sqrt(1/12)
= 0.28867513.

This distribution has the probability density function f(X) = 1.

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) at which the sparsity function
     is to be evaluated.

OUTPUT ARGUMENTS

SF   The sparsity function value.

EXAMPLES

Sample program:

program demo_unisf
use M_datapac, only : unisf, label
implicit none
   call label('unisf')
! call unisf(x,y)
end program demo_unisf

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  • Filliben, Simple and Robust Linear Estimation of the Location Parameter of a Symmetric Distribution (Unpublished PH.D. DIssertation, Princeton University), 1969, pages 21-44, 229-231.
  • Filliben, ‘The Percent Point Function’, (Unpublished Manuscript), 1970, pages 28-31.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 57-74.

Arguments

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

Source Code

SUBROUTINE UNISF(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 UNISF(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
      Sf = 1.0_wp
   ENDIF

END SUBROUTINE UNISF