t_inv.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_inv (x, n)
##
## For each component of x, compute the quantile (the inverse of the
## CDF) at x of the t (Student) distribution with parameter n.

## For very large n, the "correct" formula does not really work well,
## and the quantiles of the standard normal distribution are used
## directly.

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

function inv = t_inv (x, n)

  if (nargin != 2)
    usage ("t_inv (x, n)");
  endif

  [retval, x, n] = common_size (x, n);
  if (retval > 0)
    error ("t_inv:  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);
  inv = zeros (1, s);

  k = find ((x < 0) | (x > 1) | isnan (x) | !(n > 0));
  if any (k)
    inv(k) = NaN * ones (1, length (k));
  endif

  k = find ((x == 0) & (n > 0));
  if any (k)
    inv(k) = (-Inf) * ones (1, length (k));
  endif

  k = find ((x == 1) & (n > 0));
  if any (k)
    inv(k) = Inf * ones (1, length (k));
  endif
  
  k = find ((x > 0) & (x < 1) & (n > 0) & (n < 10000));
  if any (k)
    inv(k) = sign (x(k) - 1/2) .* sqrt (n(k) .* (1 ...
	./ beta_inv (2 * min (x(k), 1 - x(k)), n(k) / 2, 1 / 2) - 1));
  endif
  
  ## For large n, use the quantiles of the standard normal
  k = find ((x > 0) & (x < 1) & (n >= 10000));
  if any (k)
    inv(k) = stdnormal_inv (x(k));
  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");
    inv(k) = NaN * ones (1, length (k));
  endif
  
  inv = reshape (inv, r, c);
  
endfunction