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binomial_inv.m

## 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:  binomial_inv (x, n, p)
##
## For each element of x, compute the quantile at x of the binomial
## distribution with parameters n and p.

## Author:  KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description:  Quantile function of the binomial distribution

function inv = binomial_inv (x, n, p)
  
  if (nargin != 3)
    usage ("binomial_inv (x, n, p)");
  endif
  
  [retval, x, n, p] = common_size (x, n, p);
  if (retval > 0)
    error (["binomial_inv:  ", ...
          "x, n and p must be of common size or scalars"]);
  endif

  [r, c] = size (x);
  s   = r * c;
  x   = reshape (x, 1, s);
  n   = reshape (n, 1, s);
  p   = reshape (p, 1, s);
  inv = zeros (1, s);
  
  k = find (!(x >= 0) | !(x <= 1) | !(n >= 0) | (n != round (n)) ...
      | !(p >= 0) | !(p <= 1));
  if any (k)
    inv(k) = NaN * ones (1, length (k));
  endif
  
  k = find ((x >= 0) & (x <= 1) & (n >= 0) & (n == round (n)) ...
      & (p >= 0) & (p <= 1));
  if any (k)
    cdf = binomial_pdf (0, n(k), p(k));
    while (any (inv(k) < n(k)))
      m = find (cdf < x(k));
      if any (m)
      inv(k(m)) = inv(k(m)) + 1;
      cdf(m) = cdf(m) + binomial_pdf (inv(k(m)), n(k(m)), p(k(m)));
      else
      break;
      endif
    endwhile
  endif

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

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