---

C Library Functions  - causf (3)

---

NAME

causf(3f) - [M_datapac:SPARSITY] compute the Cauchy sparsity function

CONTENTS

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE CAUSF(P,Sf)

       REAL(kind=wp) :: P
       REAL(kind=wp) :: Sf

DESCRIPTION

CAUSF(3f) computes the sparsity function value for the cauchy distribution with median = 0 and 75% point = 1.

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

       function f(X) = (1/pi)*(1/(1+X*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) 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_causf
   use M_datapac, only : causf
   implicit none
   ! call causf(x,y)
   end program demo_causf

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

o	Filliben, Simple and Robust Linear Estimation of the Location Parameter of a Symmetric Distribution (Unpublished PH.D. Dissertation, Princeton University), 1969, pages 21-44, 229-231.
o	Filliben, ’The Percent Point Function’, (Unpublished manuscript), 1970, pages 28-31.
o	Johnson and Kotz, Continuous Univariate Distributions--1, 1970, pages 154-165.

---

Nemo Release 3.1

causf (3)

February 23, 2025

Generated by manServer 1.08 from 0d4cdfd4-edfe-4bfc-80c7-9c68e29ab7b7 using man macros.