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1 ## Copyright (C) 1996, 1997 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} {} discrete_inv (@var{x}, @var{v}, @var{p}) |
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21 ## For each component of @var{x}, compute the quantile (the inverse of |
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22 ## the CDF) at @var{x} of the univariate distribution which assumes the |
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23 ## values in @var{v} with probabilities @var{p}. |
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24 ## @end deftypefn |
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25 |
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26 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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27 ## Description: Quantile function of a discrete distribution |
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28 |
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29 function inv = discrete_inv (x, v, p) |
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30 |
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31 if (nargin != 3) |
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32 print_usage (); |
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33 endif |
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34 |
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35 sz = size (x); |
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36 |
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37 if (! isvector (v)) |
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38 error ("discrete_inv: v must be a vector"); |
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39 elseif (! isvector (p) || (length (p) != length (v))) |
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40 error ("discrete_inv: p must be a vector with length (v) elements"); |
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41 elseif (! (all (p >= 0) && any (p))) |
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42 error ("discrete_inv: p must be a nonzero, nonnegative vector"); |
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43 endif |
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44 |
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45 n = numel (x); |
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46 x = reshape (x, 1, n); |
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47 m = length (v); |
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48 v = sort (v); |
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49 s = reshape (cumsum (p / sum (p)), m, 1); |
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50 |
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51 ## Allow storage allocated for P to be reclaimed. |
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52 p = []; |
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53 |
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54 inv = NaN * ones (sz); |
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55 if (any (k = find (x == 0))) |
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56 inv(k) = -Inf; |
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57 endif |
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58 if (any (k = find (x == 1))) |
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59 inv(k) = v(m) * ones (size (k)); |
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60 endif |
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61 |
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62 if (any (k = find ((x > 0) & (x < 1)))) |
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63 n = length (k); |
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64 |
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65 ## The following loop is a space/time tradeoff in favor of space, |
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66 ## since the dataset may be large. |
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67 ## |
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68 ## Vectorized code is: |
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69 ## |
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70 ## inv(k) = v(sum ((ones (m, 1) * x(k)) > (s * ones (1, n))) + 1); |
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71 |
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72 for q = 1:n |
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73 inv(k(q)) = v(sum (x(k(q)) > s) + 1); |
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74 endfor |
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75 endif |
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76 |
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77 endfunction |
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78 |
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79 |
