t_cdf.m

GNU Octave is a high-level language, primarily intended for numerical computations. It provides a c

## Copyright (C) 1995, 1996, 1997  Kurt Hornik
## 
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
## 
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
## General Public License for more details. 
## 
## You should have received a copy of the GNU General Public License
## along with this file.  If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

## usage:  t_cdf (x, n)
##
## For each element of x, compute the CDF at x of the Student (t)
## distribution with n degrees of freedom, i.e., PROB( t(n) <= x ).

## Author:  KH <[e-mail]>
## Description:  CDF of the t distribution

function cdf = t_cdf (x, n)
  
  if (nargin != 2)
    usage ("t_cdf (x, n)");
  endif

  [retval, x, n] = common_size (x, n);
  if (retval > 0)
    error ("t_cdf:  x and n must be of common size or scalar");
  endif
  
  [r, c] = size (x);
  s = r * c;
  x = reshape (x, 1, s);
  n = reshape (n, 1, s);
  cdf = zeros (1, s);
  
  k = find (isnan (x) | !(n > 0));
  if any (k)
    cdf(k) = NaN * ones (1, length (k));
  endif
  
  k = find ((x == Inf) & (n > 0));
  if any (k)
    cdf(k) = ones (1, length (k));
  endif

  k = find ((x > -Inf) & (x < Inf) & (n > 0));
  if any (k)
    cdf(k) = betai (n(k) / 2, 1 / 2, 1 ./ (1 + x(k) .^ 2 ./ n(k))) / 2;
    ind = find (x(k) > 0);
    if any (ind)
      cdf(k(ind)) = 1 - cdf(k(ind));
    endif
  endif

  ## should we really only allow for positive integer n?
  k = find (n != round (n));
  if any (k)
    fprintf (stderr, ...
	     "WARNING:  n should be positive integer\n");
    cdf(k) = NaN * ones (1, length (k));
  endif

  cdf = reshape (cdf, r, c);
  
endfunction