C Library Functions - tcdf (3)

NAME

tcdf(3f) - [M_datapac:CUMULATIVE_DISTRIBUTION] computes the cumulative distribution function value for student’s t distribution with integer degrees of freedom NU.

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE TCDF(X,Nu,Cdf)

       REAL(kind=wp) :: X
       INTEGER       :: Nu
       REAL(kind=wp) :: Cdf

DESCRIPTION

TCDF(3f) computes the cumulative distribution function value for Student’s T distribution with integer degrees of freedom parameter = NU. This distribution is defined for all X.
The probability density function is given in the references below.
Note the mode of internal operations is double precision.

INPUT ARGUMENTS

X The value at which the cumulative distribution function is to be evaluated. X should be non-negative.

NU The integer number of degrees of freedom. NU should be positive.

OUTPUT ARGUMENTS

CDF The cumulative distribution function value for the Student’s T distribution

EXAMPLES

Sample program:

   program demo_tcdf
   !@(#) line plotter graph of cumulative distribution function
   use M_datapac, only : tcdf, plott, label
   implicit none
   real,allocatable  :: x(:), y(:)
   integer           :: nu
   integer           :: i
      call label(’tcdf’)
      x=[(real(i)/20.0,i=0,100,1)]
      if(allocated(y))deallocate(y)
      allocate(y(size(x)))
      nu=12
      do i=1,size(x)
         call tcdf(X(i),Nu,y(i))
      enddo
      call plott(x,y,size(x))
   end program demo_tcdf

Results:

The following is a plot of Y(I) (vertically) versus X(I) (horizontally) I-----------I-----------I-----------I-----------I 0.5000000E+01 - X 0.4791667E+01 I X 0.4583333E+01 I X 0.4375000E+01 I X 0.4166667E+01 I X 0.3958333E+01 I X 0.3750000E+01 - X 0.3541667E+01 I X 0.3333333E+01 I X 0.3125000E+01 I X 0.2916667E+01 I X 0.2708333E+01 I X 0.2500000E+01 - XX 0.2291667E+01 I X 0.2083333E+01 I X 0.1875000E+01 I XX 0.1666667E+01 I XX 0.1458333E+01 I XXX 0.1250000E+01 - XXXX 0.1041667E+01 I XXXX 0.8333335E+00 I XXXX 0.6250000E+00 I XX XX 0.4166670E+00 I X XX X 0.2083335E+00 I XX X X 0.0000000E+00 - X X X I-----------I-----------I-----------I-----------I 0.5000E+00 0.6250E+00 0.7499E+00 0.8749E+00 0.9998E+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 National Bureau of Standards Applied Mathematics Series 55, 1964, page 948, Formulae 26.7.3 and 26.7.4.

o Johnson and Kotz, Continuous Univariate Distributions--2, 1970, pages 94-129.

o Federighi, Extended Tables of the Percentage Points Of Student’S T-Distribution, Journal of the American Statistical Association, 1959, pages 683-688.

o Owen, Handbook of Statistical Tables, 1962, pages 27-30.

o Pearson and Hartley, Biometrika Tables for Statisticians, Volume 1, 1954, pages 132-134.

Nemo Release 3.1

tcdf (3)

February 23, 2025

Generated by manServer 1.08 from 471ea3a7-6f70-4d82-b673-77c69aed41d2 using man macros.

X	The value at which the cumulative distribution function is to be evaluated. X should be non-negative.
NU	The integer number of degrees of freedom. NU should be positive.

o	National Bureau of Standards Applied Mathematics Series 55, 1964, page 948, Formulae 26.7.3 and 26.7.4.
o	Johnson and Kotz, Continuous Univariate Distributions--2, 1970, pages 94-129.
o	Federighi, Extended Tables of the Percentage Points Of Student’S T-Distribution, Journal of the American Statistical Association, 1959, pages 683-688.
o	Owen, Handbook of Statistical Tables, 1962, pages 27-30.
o	Pearson and Hartley, Biometrika Tables for Statisticians, Volume 1, 1954, pages 132-134.