C Library Functions - lampdf (3)

NAME

lampdf(3f) - [M_datapac:PROBABILITY_DENSITY] compute the Tukey-Lambda probability density function

Synopsis
Description
Input Arguments
Output Arguments
Output
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE LAMPDF(X,Alamba,Pdf)

       REAL(kind=wp) :: X
       REAL(kind=wp) :: Alamba

DESCRIPTION

LAMPDF(3f) computes the probability density 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

INPUT ARGUMENTS

X The REAL value at which the probability density function is to be evaluated.
For ALAMBA non-positive, no restrictions on X.
For ALAMBA positive, X should be between (-1/ALAMBA) and (+1/ALAMBA), inclusively.

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

OUTPUT ARGUMENTS

PDF The probability density function value for the Tukey Lambda distribution

OUTPUT

EXAMPLES

Sample program:

   program demo_lampdf
   !@(#) line plotter graph of probability density function
   use M_datapac, only : lampdf, plott, label
   implicit none
   real,allocatable  :: x(:), y(:)
   real              :: alamba
   integer           :: i
      call label(’lampdf’)
      alamba=0.0
      x=[(real(i),i=-100,100,1)]
      if(allocated(y))deallocate(y)
      allocate(y(size(x)))
      do i=1,size(x)
         call LAMPDF(X(i)/100.0,Alamba,y(i))
      enddo
      call plott(x,y,size(x))
   end program demo_lampdf

Results:

The following is a plot of Y(I) (vertically) versus X(I) (horizontally) I-----------I-----------I-----------I-----------I 0.1000000E+03 - XXXX 0.9166666E+02 I XXXXXXX 0.8333334E+02 I XXXXXXX 0.7500000E+02 I XXXXXXX 0.6666667E+02 I XXXXX 0.5833334E+02 I XXXXX 0.5000000E+02 - XXXXXX 0.4166667E+02 I XXXX 0.3333334E+02 I XXXX 0.2500000E+02 I XXXX 0.1666667E+02 I XX 0.8333336E+01 I XX 0.0000000E+00 - X -0.8333328E+01 I XX -0.1666666E+02 I XX -0.2499999E+02 I XXXX -0.3333333E+02 I XXXX -0.4166666E+02 I XXXX -0.5000000E+02 - XXXXXX -0.5833333E+02 I XXXXX -0.6666666E+02 I XXXXX -0.7500000E+02 I XXXXXXX -0.8333333E+02 I XXXXXXX -0.9166666E+02 I XXXXXXX -0.1000000E+03 - XXXX I-----------I-----------I-----------I-----------I 0.1966E+00 0.2100E+00 0.2233E+00 0.2367E+00 0.2500E+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 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.

o Filliben, Simple and Robust Linear Estimation of the Location Parameter of a Symmetric Distribution (Unpublished PH.D. Dissertation, Princeton University), 1969, pages 42-44, 53-58.

Nemo Release 3.1

lampdf (3)

February 23, 2025

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