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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 2, or (at your option) |
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8 ## 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, write to the Free |
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17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} beta_inv (@var{x}, @var{a}, @var{b}) |
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22 ## For each component of @var{x}, compute the quantile (the inverse of |
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23 ## the CDF) at @var{x} of the Beta distribution with parameters @var{a} |
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24 ## and @var{b}. |
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25 ## @end deftypefn |
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26 |
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27 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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28 ## Description: Quantile function of the Beta distribution |
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29 |
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30 function inv = beta_inv (x, a, b) |
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31 |
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32 if (nargin != 3) |
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33 usage ("beta_inv (x, a, b)"); |
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34 endif |
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35 |
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36 if (!isscalar (a) || !isscalar(b)) |
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37 [retval, x, a, b] = common_size (x, a, b); |
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38 if (retval > 0) |
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39 error ("beta_inv: x, a and b must be of common size or scalars"); |
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40 endif |
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41 endif |
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42 |
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43 sz = size (x); |
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44 inv = zeros (sz); |
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45 |
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46 k = find ((x < 0) | (x > 1) | !(a > 0) | !(b > 0) | isnan (x)); |
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47 if (any (k)) |
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48 inv (k) = NaN; |
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49 endif |
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50 |
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51 k = find ((x == 1) & (a > 0) & (b > 0)); |
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52 if (any (k)) |
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53 inv (k) = 1; |
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54 endif |
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55 |
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56 k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0)); |
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57 if (any (k)) |
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58 if (!isscalar(a) || !isscalar(b)) |
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59 a = a (k); |
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60 b = b (k); |
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61 y = a ./ (a + b); |
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62 else |
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63 y = a / (a + b) * ones (size (k)); |
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64 endif |
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65 x = x (k); |
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66 l = find (y < eps); |
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67 if (any (l)) |
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68 y(l) = sqrt (eps) * ones (length (l), 1); |
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69 endif |
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70 l = find (y > 1 - eps); |
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71 if (any (l)) |
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72 y(l) = 1 - sqrt (eps) * ones (length (l), 1); |
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73 endif |
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74 |
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75 y_old = y; |
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76 for i = 1 : 10000 |
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77 h = (beta_cdf (y_old, a, b) - x) ./ beta_pdf (y_old, a, b); |
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78 y_new = y_old - h; |
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79 ind = find (y_new <= eps); |
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80 if (any (ind)) |
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81 y_new (ind) = y_old (ind) / 10; |
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82 endif |
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83 ind = find (y_new >= 1 - eps); |
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84 if (any (ind)) |
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85 y_new (ind) = 1 - (1 - y_old (ind)) / 10; |
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86 endif |
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87 h = y_old - y_new; |
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88 if (max (abs (h)) < sqrt (eps)) |
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89 break; |
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90 endif |
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91 y_old = y_new; |
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92 endfor |
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93 |
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94 inv (k) = y_new; |
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95 endif |
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96 |
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97 endfunction |
