NORSF Subroutine

public subroutine NORSF(P, Sf)

NAME

norsf(3f) - [M_datapac:SPARSITY] compute the normal sparsity function

SYNOPSIS

   SUBROUTINE NORSF(P,Sf)

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

DESCRIPTION

NORSF(3f) computes the sparsity function value for the normal
(Gaussian) distribution with mean = 0 and standard deviation = 1.

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

    f(X) = (1/sqrt(2*pi))*exp(-x*x/2)

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 at which the sparsity function is to be evaluated.
    P should be between 0.0 and 1.0, exclusively.

OUTPUT ARGUMENTS

SF  The sparsity function value.

EXAMPLES

Sample program:

program demo_norsf
use M_datapac, only : norsf
implicit none
! call norsf(x,y)
end program demo_norsf

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  • Filliben, Simple and Robust Linear Estimation of the Location Parameter of a Symmetric Distribution (Unpublished PH.D. Dissertation, Princeton University), 1969, pages 21-44, 229-231.
  • Filliben, ‘The Percent Point Function’, (Unpublished Manuscript), 1970, pages 28-31.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–1, 1970, pages 40-111.

Arguments

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

Source Code

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

REAL(kind=wp) :: c, pdf, ppf
!---------------------------------------------------------------------
      DATA c/0.3989422804_wp/
!
!     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 NORSF(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
      CALL NORPPF(P,ppf)
      pdf = c*EXP(-(ppf*ppf)/2.0_wp)
      Sf = 1.0_wp/pdf
   ENDIF
!
END SUBROUTINE NORSF