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1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
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2 ## |
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3 ## This program is free software; you can redistribute it and/or modify |
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4 ## it under the terms of the GNU General Public License as published by |
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5 ## the Free Software Foundation; either version 2, or (at your option) |
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6 ## any later version. |
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7 ## |
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8 ## This program is distributed in the hope that it will be useful, but |
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9 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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11 ## General Public License for more details. |
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12 ## |
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13 ## You should have received a copy of the GNU General Public License |
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14 ## along with this file. If not, write to the Free Software Foundation, |
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15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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16 |
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17 ## -*- texinfo -*- |
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18 ## @deftypefn {Function File} {} beta_inv (@var{x}, @var{a}, @var{b}) |
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19 ## For each component of @var{x}, compute the quantile (the inverse of |
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20 ## the CDF) at @var{x} of the Beta distribution with parameters @var{a} |
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21 ## and @var{b}. |
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22 ## @end deftypefn |
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23 |
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24 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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25 ## Description: Quantile function of the Beta distribution |
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26 |
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27 function inv = beta_inv (x, a, b) |
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28 |
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29 if (nargin != 3) |
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30 usage ("beta_inv (x, a, b)"); |
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31 endif |
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32 |
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33 [retval, x, a, b] = common_size (x, a, b); |
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34 if (retval > 0) |
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35 error ("beta_inv: x, a and b must be of common size or scalars"); |
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36 endif |
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37 |
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38 [r, c] = size (x); |
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39 s = r * c; |
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40 x = reshape (x, s, 1); |
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41 a = reshape (a, s, 1); |
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42 b = reshape (b, s, 1); |
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43 inv = zeros (s, 1); |
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44 |
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45 k = find ((x < 0) | (x > 1) | !(a > 0) | !(b > 0) | isnan (x)); |
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46 if (any (k)) |
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47 inv (k) = NaN * ones (length (k), 1); |
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48 endif |
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49 |
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50 k = find ((x == 1) & (a > 0) & (b > 0)); |
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51 if (any (k)) |
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52 inv (k) = ones (length (k), 1); |
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53 endif |
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54 |
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55 k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0)); |
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56 if (any (k)) |
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57 a = a (k); |
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58 b = b (k); |
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59 x = x (k); |
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60 y = a ./ (a + b); |
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61 l = find (y < eps); |
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62 if (any (l)) |
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63 y(l) = sqrt (eps) * ones (length (l), 1); |
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64 endif |
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65 l = find (y > 1 - eps); |
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66 if (any (l)) |
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67 y(l) = 1 - sqrt (eps) * ones (length (l), 1); |
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68 endif |
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69 |
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70 y_old = y; |
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71 for i = 1 : 10000 |
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72 h = (beta_cdf (y_old, a, b) - x) ./ beta_pdf (y_old, a, b); |
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73 y_new = y_old - h; |
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74 ind = find (y_new <= eps); |
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75 if (any (ind)) |
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76 y_new (ind) = y_old (ind) / 10; |
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77 endif |
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78 ind = find (y_new >= 1 - eps); |
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79 if (any (ind)) |
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80 y_new (ind) = 1 - (1 - y_old (ind)) / 10; |
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81 endif |
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82 h = y_old - y_new; |
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83 if (max (abs (h)) < sqrt (eps)) |
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84 break; |
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85 endif |
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86 y_old = y_new; |
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87 endfor |
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88 |
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89 inv (k) = y_new; |
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90 endif |
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91 |
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92 inv = reshape (inv, r, c); |
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93 |
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94 endfunction |
