Mercurial > octave-nkf
annotate scripts/statistics/distributions/betainv.m @ 19731:4197fc428c7d
maint: Update copyright notices for 2015.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 11 Feb 2015 14:19:08 -0500 |
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1 ## Copyright (C) 2012 Rik Wehbring |
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2 ## Copyright (C) 1995-2015 Kurt Hornik |
5410 | 3 ## |
4 ## This file is part of Octave. | |
5 ## | |
6 ## Octave is free software; you can redistribute it and/or modify it | |
7 ## under the terms of the GNU General Public License as published by | |
7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
9 ## your option) any later version. | |
5410 | 10 ## |
11 ## Octave is distributed in the hope that it will be useful, but | |
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
14 ## General Public License for more details. | |
15 ## | |
16 ## You should have received a copy of the GNU General Public License | |
7016 | 17 ## along with Octave; see the file COPYING. If not, see |
18 ## <http://www.gnu.org/licenses/>. | |
5410 | 19 |
20 ## -*- texinfo -*- | |
5411 | 21 ## @deftypefn {Function File} {} betainv (@var{x}, @var{a}, @var{b}) |
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22 ## For each element of @var{x}, compute the quantile (the inverse of |
5410 | 23 ## the CDF) at @var{x} of the Beta distribution with parameters @var{a} |
24 ## and @var{b}. | |
25 ## @end deftypefn | |
26 | |
5428 | 27 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
5410 | 28 ## Description: Quantile function of the Beta distribution |
29 | |
5411 | 30 function inv = betainv (x, a, b) |
5410 | 31 |
32 if (nargin != 3) | |
6046 | 33 print_usage (); |
5410 | 34 endif |
35 | |
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36 if (!isscalar (a) || !isscalar (b)) |
5410 | 37 [retval, x, a, b] = common_size (x, a, b); |
38 if (retval > 0) | |
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39 error ("betainv: X, A, and B must be of common size or scalars"); |
5410 | 40 endif |
41 endif | |
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42 |
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43 if (iscomplex (x) || iscomplex (a) || iscomplex (b)) |
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44 error ("betainv: X, A, and B must not be complex"); |
5410 | 45 endif |
46 | |
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47 if (isa (x, "single") || isa (a, "single") || isa (b, "single")) |
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48 inv = zeros (size (x), "single"); |
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49 else |
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50 inv = zeros (size (x)); |
5410 | 51 endif |
52 | |
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53 k = (x < 0) | (x > 1) | !(a > 0) | !(b > 0) | isnan (x); |
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54 inv(k) = NaN; |
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55 |
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56 k = (x == 1) & (a > 0) & (b > 0); |
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57 inv(k) = 1; |
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58 |
5410 | 59 k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0)); |
60 if (any (k)) | |
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61 if (!isscalar (a) || !isscalar (b)) |
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62 a = a(k); |
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63 b = b(k); |
5410 | 64 y = a ./ (a + b); |
65 else | |
66 y = a / (a + b) * ones (size (k)); | |
67 endif | |
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68 x = x(k); |
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69 |
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70 if (isa (y, "single")) |
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71 myeps = eps ("single"); |
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72 else |
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73 myeps = eps; |
5410 | 74 endif |
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75 |
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76 l = find (y < myeps); |
5410 | 77 if (any (l)) |
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78 y(l) = sqrt (myeps) * ones (length (l), 1); |
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79 endif |
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80 l = find (y > 1 - myeps); |
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81 if (any (l)) |
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82 y(l) = 1 - sqrt (myeps) * ones (length (l), 1); |
5410 | 83 endif |
84 | |
85 y_old = y; | |
86 for i = 1 : 10000 | |
5411 | 87 h = (betacdf (y_old, a, b) - x) ./ betapdf (y_old, a, b); |
5410 | 88 y_new = y_old - h; |
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89 ind = find (y_new <= myeps); |
5410 | 90 if (any (ind)) |
91 y_new (ind) = y_old (ind) / 10; | |
92 endif | |
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93 ind = find (y_new >= 1 - myeps); |
5410 | 94 if (any (ind)) |
95 y_new (ind) = 1 - (1 - y_old (ind)) / 10; | |
96 endif | |
97 h = y_old - y_new; | |
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98 if (max (abs (h)) < sqrt (myeps)) |
5410 | 99 break; |
100 endif | |
101 y_old = y_new; | |
102 endfor | |
103 | |
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104 inv(k) = y_new; |
5410 | 105 endif |
106 | |
107 endfunction | |
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108 |
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109 |
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110 %!shared x |
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111 %! x = [-1 0 0.75 1 2]; |
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112 %!assert (betainv (x, ones (1,5), 2*ones (1,5)), [NaN 0 0.5 1 NaN]) |
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113 %!assert (betainv (x, 1, 2*ones (1,5)), [NaN 0 0.5 1 NaN]) |
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114 %!assert (betainv (x, ones (1,5), 2), [NaN 0 0.5 1 NaN]) |
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115 %!assert (betainv (x, [1 0 NaN 1 1], 2), [NaN NaN NaN 1 NaN]) |
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116 %!assert (betainv (x, 1, 2*[1 0 NaN 1 1]), [NaN NaN NaN 1 NaN]) |
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117 %!assert (betainv ([x(1:2) NaN x(4:5)], 1, 2), [NaN 0 NaN 1 NaN]) |
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118 |
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119 %% Test class of input preserved |
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120 %!assert (betainv ([x, NaN], 1, 2), [NaN 0 0.5 1 NaN NaN]) |
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121 %!assert (betainv (single ([x, NaN]), 1, 2), single ([NaN 0 0.5 1 NaN NaN])) |
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122 %!assert (betainv ([x, NaN], single (1), 2), single ([NaN 0 0.5 1 NaN NaN])) |
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123 %!assert (betainv ([x, NaN], 1, single (2)), single ([NaN 0 0.5 1 NaN NaN])) |
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124 |
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125 %% Test input validation |
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126 %!error betainv () |
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127 %!error betainv (1) |
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128 %!error betainv (1,2) |
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129 %!error betainv (1,2,3,4) |
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130 %!error betainv (ones (3), ones (2), ones (2)) |
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131 %!error betainv (ones (2), ones (3), ones (2)) |
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132 %!error betainv (ones (2), ones (2), ones (3)) |
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133 %!error betainv (i, 2, 2) |
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134 %!error betainv (2, i, 2) |
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135 %!error betainv (2, 2, i) |
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136 |