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qqplot.m: Plot points as well as connecting line. * qqplot.m: Plot points as well as connecting line.
author Rik <rik@octave.org>
date Sun, 02 Feb 2014 22:21:45 -0800
parents d63878346099
children 0e1f5a750d00
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rev   line source
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1 ## Copyright (C) 1995-2013 Kurt Hornik
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {[@var{q}, @var{s}] =} qqplot (@var{x})
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21 ## @deftypefnx {Function File} {[@var{q}, @var{s}] =} qqplot (@var{x}, @var{y})
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22 ## @deftypefnx {Function File} {[@var{q}, @var{s}] =} qqplot (@var{x}, @var{dist})
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23 ## @deftypefnx {Function File} {[@var{q}, @var{s}] =} qqplot (@var{x}, @var{y}, @var{params})
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24 ## @deftypefnx {Function File} {} qqplot (@dots{})
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25 ## Perform a QQ-plot (quantile plot).
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26 ##
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27 ## If F is the CDF of the distribution @var{dist} with parameters
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28 ## @var{params} and G its inverse, and @var{x} a sample vector of length
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29 ## @var{n}, the QQ-plot graphs ordinate @var{s}(@var{i}) = @var{i}-th
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30 ## largest element of x versus abscissa @var{q}(@var{i}f) = G((@var{i} -
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31 ## 0.5)/@var{n}).
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32 ##
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33 ## If the sample comes from F, except for a transformation of location
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34 ## and scale, the pairs will approximately follow a straight line.
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35 ##
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36 ## If the second argument is a vector @var{y} the empirical CDF of @var{y}
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37 ## is used as @var{dist}.
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38 ##
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39 ## The default for @var{dist} is the standard normal distribution. The
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40 ## optional argument @var{params} contains a list of parameters of
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41 ## @var{dist}. For example, for a quantile plot of the uniform
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42 ## distribution on [2,4] and @var{x}, use
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43 ##
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44 ## @example
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45 ## qqplot (x, "unif", 2, 4)
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46 ## @end example
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47 ##
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48 ## @noindent
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49 ## @var{dist} can be any string for which a function @var{distinv} or
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50 ## @var{dist_inv} exists that calculates the inverse CDF of distribution
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51 ## @var{dist}.
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52 ##
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53 ## If no output arguments are given, the data are plotted directly.
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54 ## @end deftypefn
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55
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56 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
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57 ## Description: Perform a QQ-plot (quantile plot)
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58
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59 function [qout, sout] = qqplot (x, dist, varargin)
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60
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61 if (nargin < 1)
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62 print_usage ();
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63 endif
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64
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65 if (! (isnumeric (x) && isvector (x)))
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66 error ("qqplot: X must be a numeric vector");
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67 endif
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68
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69 if (nargin == 1)
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70 f = @stdnormal_inv;
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71 else
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72 if (isnumeric (dist))
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73 f = @(y) empirical_inv (y, dist);
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74 elseif (ischar (dist) && (exist (invname = [dist "inv"])
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75 || exist (invname = [dist "%s_inv"])))
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76 f = str2func (invname);
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77 else
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78 error ("qqplot: no inverse CDF found for distribution DIST");
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79 endif
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80 endif;
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81
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82 s = sort (x);
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83 n = length (x);
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84 t = ((1 : n)' - .5) / n;
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85 if (nargin <= 2)
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86 q = f (t);
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87 q_label = func2str (f);
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88 else
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89 q = f (t, varargin{:});
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90 if (nargin == 3)
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91 q_label = sprintf ("%s with parameter %g", func2str (f), varargin{1});
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92 else
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93 q_label = sprintf ("%s with parameters %g", func2str (f), varargin{1});
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94 param_str = sprintf (", %g", varargin{2:end});
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95 q_label = [q_label param_str];
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96 endif
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97 endif
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98
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99 if (nargout == 0)
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100 plot (q, s, "-x");
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101 q_label = strrep (q_label, '_inv', '\_inv');
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102 if (q_label(1) == '@')
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103 q_label = q_label(6:end); # Strip "@(y) " from anon. function
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104 endif
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105 xlabel (q_label);
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106 ylabel ("sample points");
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107 else
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108 qout = q;
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109 sout = s;
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110 endif
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111
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112 endfunction
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113