Mercurial > octave-nkf
annotate scripts/statistics/distributions/wblcdf.m @ 20643:d6d04088ac9e
nbininv.m: Increase speed (85X) and accuracy of function (bug #34363).
* nbininv.m: Call new function scalar_nbininv to calculate nbininv for scalar.
If there are still uncalculated values then call bin_search_nbininv. Call
bin_search_nbininv directly for vectors. Add more BIST tests.
* nbininv.m (scalar_binoinv): New subfunction to calculate nbininv for scalar x.
Stops when x > 1000.
* nbininv.m (bin_search_nbininv): New subfunction to do binary search for nbininv.
author | Lachlan Andrew <lachlanbis@gmail.com> |
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date | Sun, 11 Oct 2015 20:33:37 -0700 |
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1 ## Copyright (C) 2012 Rik Wehbring |
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2 ## Copyright (C) 1995-2015 Kurt Hornik |
5693 | 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. | |
5693 | 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/>. | |
5693 | 19 |
20 ## -*- texinfo -*- | |
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21 ## @deftypefn {Function File} {} wblcdf (@var{x}) |
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22 ## @deftypefnx {Function File} {} wblcdf (@var{x}, @var{scale}) |
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23 ## @deftypefnx {Function File} {} wblcdf (@var{x}, @var{scale}, @var{shape}) |
5693 | 24 ## Compute the cumulative distribution function (CDF) at @var{x} of the |
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25 ## Weibull distribution with scale parameter @var{scale} and shape |
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26 ## parameter @var{shape}. |
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27 ## |
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28 ## This is defined as |
6754 | 29 ## @tex |
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30 ## $$ 1 - e^{-({x \over scale})^{shape}} $$ |
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31 ## for $x \geq 0$. |
6754 | 32 ## @end tex |
33 ## @ifnottex | |
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34 ## |
5693 | 35 ## @example |
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36 ## 1 - exp (-(x/scale)^shape) |
5693 | 37 ## @end example |
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38 ## |
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39 ## @noindent |
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40 ## for @var{x} @geq{} 0. |
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41 ## |
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42 ## Default values are @var{scale} = 1, @var{shape} = 1. |
6754 | 43 ## @end ifnottex |
5693 | 44 ## @end deftypefn |
45 | |
46 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> | |
47 ## Description: CDF of the Weibull distribution | |
48 | |
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49 function cdf = wblcdf (x, scale = 1, shape = 1) |
5693 | 50 |
51 if (nargin < 1 || nargin > 3) | |
6046 | 52 print_usage (); |
5693 | 53 endif |
54 | |
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55 if (! isscalar (shape) || ! isscalar (scale)) |
5693 | 56 [retval, x, shape, scale] = common_size (x, shape, scale); |
57 if (retval > 0) | |
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58 error ("wblcdf: X, SCALE, and SHAPE must be of common size or scalars"); |
5693 | 59 endif |
60 endif | |
61 | |
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62 if (iscomplex (x) || iscomplex (scale) || iscomplex (shape)) |
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63 error ("wblcdf: X, SCALE, and SHAPE must not be complex"); |
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64 endif |
5693 | 65 |
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66 if (isa (x, "single") || isa (scale, "single") || isa (shape, "single")) |
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67 cdf = NaN (size (x), "single"); |
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68 else |
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69 cdf = NaN (size (x)); |
5693 | 70 endif |
71 | |
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72 ok = (shape > 0) & (shape < Inf) & (scale > 0) & (scale < Inf); |
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73 |
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74 k = (x <= 0) & ok; |
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75 cdf(k) = 0; |
5693 | 76 |
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77 k = (x == Inf) & ok; |
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78 cdf(k) = 1; |
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79 |
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80 k = (x > 0) & (x < Inf) & ok; |
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81 if (isscalar (shape) && isscalar (scale)) |
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82 cdf(k) = 1 - exp (- (x(k) / scale) .^ shape); |
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83 else |
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84 cdf(k) = 1 - exp (- (x(k) ./ scale(k)) .^ shape(k)); |
5693 | 85 endif |
86 | |
87 endfunction | |
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88 |
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89 |
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90 %!shared x,y |
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91 %! x = [-1 0 0.5 1 Inf]; |
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92 %! y = [0, 1-exp(-x(2:4)), 1]; |
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93 %!assert (wblcdf (x, ones (1,5), ones (1,5)), y) |
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94 %!assert (wblcdf (x, 1, ones (1,5)), y) |
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95 %!assert (wblcdf (x, ones (1,5), 1), y) |
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96 %!assert (wblcdf (x, [0 1 NaN Inf 1], 1), [NaN 0 NaN NaN 1]) |
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97 %!assert (wblcdf (x, 1, [0 1 NaN Inf 1]), [NaN 0 NaN NaN 1]) |
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98 %!assert (wblcdf ([x(1:2) NaN x(4:5)], 1, 1), [y(1:2) NaN y(4:5)]) |
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99 |
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100 ## Test class of input preserved |
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101 %!assert (wblcdf ([x, NaN], 1, 1), [y, NaN]) |
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102 %!assert (wblcdf (single ([x, NaN]), 1, 1), single ([y, NaN])) |
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103 %!assert (wblcdf ([x, NaN], single (1), 1), single ([y, NaN])) |
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104 %!assert (wblcdf ([x, NaN], 1, single (1)), single ([y, NaN])) |
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105 |
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106 ## Test input validation |
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107 %!error wblcdf () |
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108 %!error wblcdf (1,2,3,4) |
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109 %!error wblcdf (ones (3), ones (2), ones (2)) |
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110 %!error wblcdf (ones (2), ones (3), ones (2)) |
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111 %!error wblcdf (ones (2), ones (2), ones (3)) |
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112 %!error wblcdf (i, 2, 2) |
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113 %!error wblcdf (2, i, 2) |
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114 %!error wblcdf (2, 2, i) |
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115 |