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scripts/statistics/distributions/cauchy_inv.m

changeset 10289: 4b124317dc38
parent:93c65f2a5668
author: John W. Eaton <jwe@octave.org>
date: Tue Feb 09 20:58:55 2010 -0500 (47 minutes ago)
permissions: -rw-r--r--
description: base_properties::set_children: account for hidden children 
     1## Copyright (C) 1995, 1996, 1997, 1998, 2000, 2002, 2004, 2005, 2006,

     2##               2007 Kurt Hornik

     3##

     4## This file is part of Octave.

     5##

     6## Octave is free software; you can redistribute it and/or modify it

     7## under the terms of the GNU General Public License as published by

     8## the Free Software Foundation; either version 3 of the License, or (at

     9## your option) any later version.

    10##

    11## Octave is distributed in the hope that it will be useful, but

    12## WITHOUT ANY WARRANTY; without even the implied warranty of

    13## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

    14## General Public License for more details.

    15##

    16## You should have received a copy of the GNU General Public License

    17## along with Octave; see the file COPYING.  If not, see

    18## <http://www.gnu.org/licenses/>.

    19

    20## -*- texinfo -*-

    21## @deftypefn {Function File} {} cauchy_inv (@var{x}, @var{lambda}, @var{sigma})

    22## For each element of @var{x}, compute the quantile (the inverse of the

    23## CDF) at @var{x} of the Cauchy distribution with location parameter

    24## @var{lambda} and scale parameter @var{sigma}.  Default values are

    25## @var{lambda} = 0, @var{sigma} = 1. 

    26## @end deftypefn

    27

    28## Author: KH <Kurt.Hornik@wu-wien.ac.at>

    29## Description: Quantile function of the Cauchy distribution

    30

    31function inv = cauchy_inv (x, location, scale)

    32

    33  if (! (nargin == 1 || nargin == 3))

    34    print_usage ();

    35  endif

    36

    37  if (nargin == 1)

    38    location = 0;

    39    scale = 1;

    40  endif

    41

    42  if (!isscalar (location) || !isscalar (scale)) 

    43    [retval, x, location, scale] = common_size (x, location, scale);

    44    if (retval > 0)

    45      error ("cauchy_inv: x, lambda and sigma must be of common size or scalar");

    46    endif

    47  endif

    48

    49  sz = size (x);

    50  inv = NaN * ones (sz);

    51

    52  ok = ((location > -Inf) & (location < Inf) &

    53       (scale > 0) & (scale < Inf));

    54

    55  k = find ((x == 0) & ok);

    56  if (any (k))

    57    inv(k) = -Inf;

    58  endif

    59

    60  k = find ((x > 0) & (x < 1) & ok);

    61  if (any (k))

    62    if (isscalar (location) && isscalar (scale)) 

    63      inv(k) = location - scale .* cot (pi * x(k));

    64    else

    65      inv(k) = location(k) - scale(k) .* cot (pi * x(k));

    66    endif

    67  endif

    68

    69  k = find ((x == 1) & ok);

    70  if (any (k))

    71    inv(k) = Inf;

    72  endif

    73

    74endfunction