C Library Functions - lamppf (3)

NAME

lamppf(3f) - [M_datapac:PERCENT_POINT] compute the Tukey-Lambda percent point function

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE LAMPPF(P,Alamba,Ppf)

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

DESCRIPTION

LAMPPF(3f) computes the percent point 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 percent point function of a distribution is identically the same as the inverse cumulative distribution function of the distribution.

INPUT ARGUMENTS

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

ALAMBA The value of lambda (the tail length parameter).

OUTPUT ARGUMENTS

PPF The percent point function value ppf for the Tukey lambda distribution

EXAMPLES

Sample program:

   program demo_lamppf
   !@(#) line plotter graph of function
   use M_datapac, only : lamppf, plott, label
   implicit none
   integer,parameter :: n=200
   real              :: x(n), y(n)
   real              :: alamba
   integer           :: i
      alamba=3.3333
      call label(’lamppf’)
      x=[(real(i)/real(n+1),i=1,n)]
      do i=1,n
         call lamppf(x(i),alamba,y(i))
      enddo
      call plott(x,y,n)
   end program demo_lamppf

Results:

The following is a plot of Y(I) (vertically) versus X(I) (horizontally) I-----------I-----------I-----------I-----------I 0.9950249E+00 - XXX 0.9537728E+00 I XXX 0.9125207E+00 I XXX 0.8712686E+00 I XXXX 0.8300166E+00 I XXX 0.7887645E+00 I XXX 0.7475125E+00 - XXX 0.7062603E+00 I XXX 0.6650083E+00 I XX 0.6237562E+00 I XX 0.5825042E+00 I XX 0.5412520E+00 I XX 0.5000000E+00 - XXX 0.4587479E+00 I XX 0.4174958E+00 I XX 0.3762438E+00 I XX 0.3349917E+00 I XX 0.2937396E+00 I XXX 0.2524875E+00 - XXX 0.2112355E+00 I XXX 0.1699834E+00 I XXX 0.1287313E+00 I XXXX 0.8747923E-01 I XXX 0.4622716E-01 I XXX 0.4975124E-02 - XXX I-----------I-----------I-----------I-----------I -0.2951E+00 -0.1475E+00 0.0000E+00 0.1475E+00 0.2951E+00

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

lamppf (3)

July 22, 2023

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