C Library Functions  - lamsf (3)

NAME
lamsf(3f) - [M_datapac:SPARSITY] compute the Tukey-Lambda sparsity function

CONTENTS

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS
SUBROUTINE LAMSF(P,Alamba,Sf) 

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

DESCRIPTION
LAMSF(3f) computes the sparsity function value for the (Tukey) lambda distribution with tail length parameter value = ALAMBA.

In general, the probability density function for this distribution is not simple.

The percent point function for this distribution is 

       g(P) = ((P**ALAMBA)-((1-P)**ALAMBA))/ALAMBA
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.
ALAMBA The value of Lambda (the Tail Length parameter). 

           If ALAMBA is positive, then P should be between 0.0 and 1.0,
           inclusively.


           If ALAMBA is non-positive, then P should be between 0.0 and
           1.0, exclusively.

OUTPUT ARGUMENTS

SF The sparsity function value for the Tukey Lambda distribution

EXAMPLES
Sample program: 

   program demo_lamsf
   use M_datapac, only : lamsf
   implicit none
   ! call lamsf(x,y)
   end program demo_lamsf
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o Filliben, Simple and Robust Linear Estimation of the Location Parameter of a Symmetric Distribution (Unpublished PH.D. Dissertation, Princeton University), 1969, pages 21-44, 229-231, pages 53-58.
o Filliben, ’The Percent Point Function’, (Unpublished Manuscript), 1970, pages 28-31.
o Hastings, Mosteller, Tukey, and Windsor, ’Low Moments for Small
Samples:
  A Comparative Study of Order Statistics’, Annals of Mathematical Statistics, 18, 1947, pages 413-426.

Nemo Release 3.1 lamsf (3) July 22, 2023
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