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1 ## Copyright (C) 1995, 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} {} cauchy_inv (@var{x}, @var{lambda}, @var{sigma}) |
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21 ## For each element of @var{x}, compute the quantile (the inverse of the |
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22 ## CDF) at @var{x} of the Cauchy distribution with location parameter |
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23 ## @var{lambda} and scale parameter @var{sigma}. Default values are |
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24 ## @var{lambda} = 0, @var{sigma} = 1. |
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25 ## @end deftypefn |
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26 |
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27 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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28 ## Description: Quantile function of the Cauchy distribution |
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29 |
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30 function inv = cauchy_inv (x, location, scale) |
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31 |
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32 if (! (nargin == 1 || nargin == 3)) |
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33 print_usage (); |
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34 endif |
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35 |
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36 if (nargin == 1) |
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37 location = 0; |
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38 scale = 1; |
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39 endif |
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40 |
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41 if (!isscalar (location) || !isscalar (scale)) |
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42 [retval, x, location, scale] = common_size (x, location, scale); |
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43 if (retval > 0) |
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44 error ("cauchy_inv: x, lambda and sigma must be of common size or scalar"); |
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45 endif |
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46 endif |
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47 |
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48 sz = size (x); |
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49 inv = NaN * ones (sz); |
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50 |
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51 ok = ((location > -Inf) & (location < Inf) & |
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52 (scale > 0) & (scale < Inf)); |
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53 |
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54 k = find ((x == 0) & ok); |
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55 if (any (k)) |
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56 inv(k) = -Inf; |
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57 endif |
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58 |
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59 k = find ((x > 0) & (x < 1) & ok); |
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60 if (any (k)) |
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61 if (isscalar (location) && isscalar (scale)) |
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62 inv(k) = location - scale .* cot (pi * x(k)); |
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63 else |
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64 inv(k) = location(k) - scale(k) .* cot (pi * x(k)); |
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65 endif |
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66 endif |
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67 |
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68 k = find ((x == 1) & ok); |
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69 if (any (k)) |
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70 inv(k) = Inf; |
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71 endif |
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72 |
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73 endfunction |
