poisson_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:  poisson_inv (x, lambda)
##
## For each component of x, compute the quantile (the inverse of the
## CDF) at x of the Poisson distribution with parameter lambda.

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

function inv = poisson_inv (x, l)
  
  if (nargin != 2)
    usage ("poisson_inv (x, lambda)");
  endif

  [retval, x, l] = common_size (x, l);
  if (retval > 0)
    error (["poisson_inv:  ", ...
	    "x and lambda must be of common size or scalar"]);
  endif
  
  [r, c] = size (x);
  s = r * c;
  x = reshape (x, 1, s);
  l = reshape (l, 1, s);
  inv = zeros (1, s);

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

  k = find ((x == 1) & (l > 0));
  if any (k)
    inv(k) = Inf * ones (1, length (k));
  endif
  
  k = find ((x > 0) & (x < 1) & (l > 0));
  if any (k)
    cdf = exp (-l(k));
    while (1)
      m = find (cdf < x(k));
      if any (m)
	inv(k(m)) = inv(k(m)) + 1;
	cdf(m) = cdf(m) + poisson_pdf (inv(k(m)), l(k(m)));
      else
	break;
      endif
    endwhile
  endif
    
  inv = reshape (inv, r, c);
  
endfunction