C Library Functions - lamcdf (3)

NAME

lamcdf(3f) - [M_datapac:CUMULATIVE_DISTRIBUTION] compute the Tukey-Lambda cumulative distribution function

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE LAMCDF(X,Alamba,Cdf)

       REAL(kind=wp),intent(in)  :: X
       REAL(kind=wp),intent(in)  :: Alamba
       REAL(kind=wp),intent(out) :: Cdf

DESCRIPTION

LAMCDF(3f) computes the cumulative distribution 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 value at which the cumulative distribution 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 value of lambda (the tail length parameter).

OUTPUT ARGUMENTS

CDF The cumulative distribution function value for the Tukey lambda distribution.

EXAMPLES

Sample program:

   program demo_lamcdf
   !@(#) line plotter graph of cumulative distribution function
   use M_datapac, only : lamcdf, plott, label
   implicit none
   real,allocatable  :: x(:), y(:)
   real              :: alamba
   integer           :: i
      call label(’lamcdf’)
      alamba=4.0
      x=[(real(i)/100.0/alamba,i=-100,100,1)]
      if(allocated(y))deallocate(y)
      allocate(y(size(x)))
      do i=1,size(x)
         call lamcdf(X(i),Alamba,y(i))
      enddo
      call plott(x,y,size(x))
   end program demo_lamcdf

Results:

The following is a plot of Y(I) (vertically) versus X(I) (horizontally) I-----------I-----------I-----------I-----------I 0.2500000E+00 - X 0.2291667E+00 I XX 0.2083333E+00 I XX 0.1875000E+00 I XX 0.1666667E+00 I XX 0.1458333E+00 I XXX 0.1250000E+00 - XX 0.1041667E+00 I XX 0.8333333E-01 I XX 0.6250000E-01 I XXX 0.4166666E-01 I XXXX 0.2083333E-01 I XXXX 0.0000000E+00 - XXXXX -0.2083334E-01 I XXXX -0.4166669E-01 I XXXX -0.6250000E-01 I XXX -0.8333334E-01 I XX -0.1041667E+00 I XX -0.1250000E+00 - XX -0.1458333E+00 I XXX -0.1666667E+00 I XX -0.1875000E+00 I XX -0.2083333E+00 I XX -0.2291667E+00 I XX -0.2500000E+00 - X I-----------I-----------I-----------I-----------I 0.0000E+00 0.2500E+00 0.5000E+00 0.7500E+00 0.1000E+01

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

lamcdf (3)

February 23, 2025

Generated by manServer 1.08 from 5a5c1914-836f-4e6b-8406-2420e2ee9041 using man macros.

X	The value at which the cumulative distribution 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 value of lambda (the tail length parameter).