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comparison scripts/statistics/distributions/gamma_inv.m @ 3426:f8dde1807dee

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[project @ 2000-01-13 08:40:00 by jwe]
author jwe
date Thu, 13 Jan 2000 08:40:53 +0000
parents e4f4b2d26ee9
children 434790acb067
comparison
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3425:8625164a0a39 3426:f8dde1807dee
1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik 1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik
2 ## 2 ##
3 ## This program is free software; you can redistribute it and/or modify 3 ## This program is free software; you can redistribute it and/or modify
4 ## it under the terms of the GNU General Public License as published by 4 ## it under the terms of the GNU General Public License as published by
5 ## the Free Software Foundation; either version 2, or (at your option) 5 ## the Free Software Foundation; either version 2, or (at your option)
6 ## any later version. 6 ## any later version.
7 ## 7 ##
8 ## This program is distributed in the hope that it will be useful, but 8 ## This program is distributed in the hope that it will be useful, but
9 ## WITHOUT ANY WARRANTY; without even the implied warranty of 9 ## WITHOUT ANY WARRANTY; without even the implied warranty of
10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
11 ## General Public License for more details. 11 ## General Public License for more details.
12 ## 12 ##
13 ## You should have received a copy of the GNU General Public License 13 ## You should have received a copy of the GNU General Public License
14 ## along with this file. If not, write to the Free Software Foundation, 14 ## along with this file. If not, write to the Free Software Foundation,
15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. 15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
16 16
17 ## usage: gamma_inv (x, a, b) 17 ## usage: gamma_inv (x, a, b)
18 ## 18 ##
19 ## For each component of x, compute the quantile (the inverse of the 19 ## For each component of x, compute the quantile (the inverse of the
20 ## CDF) at x of the Gamma distribution with parameters a and b. 20 ## CDF) at x of the Gamma distribution with parameters a and b.
21 21
22 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> 22 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
23 ## Description: Quantile function of the Gamma distribution 23 ## Description: Quantile function of the Gamma distribution
24 24
25 function inv = gamma_inv (x, a, b) 25 function inv = gamma_inv (x, a, b)
26 26
27 if (nargin != 3) 27 if (nargin != 3)
28 usage ("gamma_inv (x, a, b)"); 28 usage ("gamma_inv (x, a, b)");
29 endif 29 endif
30 30
31 [retval, x, a, b] = common_size (x, a, b); 31 [retval, x, a, b] = common_size (x, a, b);
32 if (retval > 0) 32 if (retval > 0)
33 error ("gamma_inv: x, a and b must be of common size or scalars"); 33 error ("gamma_inv: x, a and b must be of common size or scalars");
34 endif 34 endif
35 35
37 s = r * c; 37 s = r * c;
38 x = reshape (x, s, 1); 38 x = reshape (x, s, 1);
39 a = reshape (a, s, 1); 39 a = reshape (a, s, 1);
40 b = reshape (b, s, 1); 40 b = reshape (b, s, 1);
41 inv = zeros (s, 1); 41 inv = zeros (s, 1);
42 42
43 k = find ((x < 0) | (x > 1) | isnan (x) | !(a > 0) | !(b > 0)); 43 k = find ((x < 0) | (x > 1) | isnan (x) | !(a > 0) | !(b > 0));
44 if any (k) 44 if any (k)
45 inv (k) = NaN * ones (length (k), 1); 45 inv (k) = NaN * ones (length (k), 1);
46 endif 46 endif
47 47
48 k = find ((x == 1) & (a > 0) & (b > 0)); 48 k = find ((x == 1) & (a > 0) & (b > 0));
49 if any (k) 49 if any (k)
50 inv (k) = Inf * ones (length (k), 1); 50 inv (k) = Inf * ones (length (k), 1);
51 endif 51 endif
52 52
53 k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0)); 53 k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0));
54 if any (k) 54 if any (k)
55 a = a (k); 55 a = a (k);
56 b = b (k); 56 b = b (k);
57 x = x (k); 57 x = x (k);
65 for i = 1 : 100 65 for i = 1 : 100
66 h = (gamma_cdf (y_old, a, b) - x) ./ gamma_pdf (y_old, a, b); 66 h = (gamma_cdf (y_old, a, b) - x) ./ gamma_pdf (y_old, a, b);
67 y_new = y_old - h; 67 y_new = y_old - h;
68 ind = find (y_new <= eps); 68 ind = find (y_new <= eps);
69 if (any (ind)) 69 if (any (ind))
70 y_new (ind) = y_old (ind) / 10; 70 y_new (ind) = y_old (ind) / 10;
71 h = y_old - y_new; 71 h = y_old - y_new;
72 endif 72 endif
73 if (max (abs (h)) < sqrt (eps)) 73 if (max (abs (h)) < sqrt (eps))
74 break; 74 break;
75 endif 75 endif
76 y_old = y_new; 76 y_old = y_new;
77 endfor 77 endfor
78 78
79 inv (k) = y_new; 79 inv (k) = y_new;
80 endif 80 endif
81 81
82 inv = reshape (inv, r, c); 82 inv = reshape (inv, r, c);
83 83
84 endfunction 84 endfunction