/usr/share/octave/packages/statistics-1.3.0/gpcdf.m is in octave-statistics 1.3.0-1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 | ## Copyright (C) 2016 Dag Lyberg
## Copyright (C) 1997-2015 Kurt Hornik
##
## This file is part of Octave.
##
## Octave is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or (at
## your option) any later version.
##
## Octave is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {} {} gpcdf (@var{x}, @var{location}, @var{scale}, @var{shape})
## Compute the cumulative distribution function (CDF) at @var{x} of the
## generalized Pareto distribution with parameters @var{location}, @var{scale},
## and @var{shape}.
## @end deftypefn
## Author: Dag Lyberg <daglyberg80@gmail.com>
## Description: PDF of the generalized Pareto distribution
function cdf = gpcdf (x, location, scale, shape)
if (nargin != 4)
print_usage ();
endif
if (! isscalar (location) || ! isscalar (scale) || ! isscalar (shape))
[retval, x, location, scale, shape] = ...
common_size (x, location, scale, shape);
if (retval > 0)
error ("gpcdf: X, LOCATION, SCALE and SHAPE must be of common size or scalars");
endif
endif
if (iscomplex (x) || iscomplex (location) || iscomplex (scale) ...
|| iscomplex (shape))
error ("gpcdf: X, LOCATION, SCALE and SHAPE must not be complex");
endif
if (isa (x, "single") || isa (location, "single") || isa (scale, "single") ...
|| isa (shape, "single"))
cdf = zeros (size (x), "single");
else
cdf = zeros (size (x));
endif
k = isnan (x) | ! (-Inf < location) | ! (location < Inf) | ! (scale > 0) ...
| ! (-Inf < shape) | ! (shape < Inf);
cdf(k) = NaN;
k = (x == Inf) & (-Inf < location) & (location < Inf) & (scale > 0) ...
& (-Inf < shape) & (shape < Inf);
cdf(k) = 1;
k = (-Inf < x) & (x < Inf) & (-Inf < location) & (location < Inf) ...
& (scale > 0) & (scale < Inf) & (-Inf < shape) & (shape < Inf);
if (isscalar (location) && isscalar (scale) && isscalar (shape))
z = (x - location) / scale;
j = k & (shape == 0) & (z >= 0);
if (any (j))
cdf(j) = 1 - exp (-z(j));
endif
j = k & (shape > 0) & (z >= 0);
if (any (j))
cdf(j) = 1 - (shape * z(j) + 1).^(-1 / shape);
endif
if (shape < 0)
j = k & (shape < 0) & (0 <= z) & (z <= -1 ./ shape);
if (any (j))
cdf(j) = 1 - (shape * z(j) + 1).^(-1 / shape);
endif
endif
else
z = (x - location) ./ scale;
j = k & (shape == 0) & (z >= 0);
if (any (j))
cdf(j) = 1 - exp (-z(j));
endif
j = k & (shape > 0) & (z >= 0);
if (any (j))
cdf(j) = 1 - (shape(j) .* z(j) + 1).^(-1 ./ shape(j));
endif
if (any (shape < 0))
j = k & (shape < 0) & (0 <= z) & (z <= -1 ./ shape);
if (any (j))
cdf(j) = 1 - (shape(j) .* z(j) + 1).^(-1 ./ shape(j));
endif
endif
endif
endfunction
%!shared x,y1,y2,y3
%! x = [-Inf, -1, 0, 1/2, 1, Inf];
%! y1 = [0, 0, 0, 0.3934693402873666, 0.6321205588285577, 1];
%! y2 = [0, 0, 0, 1/3, 1/2, 1];
%! y3 = [0, 0, 0, 1/2, 1, 1];
%! seps = eps('single')*5;
%!assert (gpcdf (x, zeros (1,6), ones (1,6), zeros (1,6)), y1, eps)
%!assert (gpcdf (x, zeros (1,6), 1, 0), y1, eps)
%!assert (gpcdf (x, 0, ones (1,6), 0), y1, eps)
%!assert (gpcdf (x, 0, 1, zeros (1,6)), y1, eps)
%!assert (gpcdf (x, 0, 1, 0), y1, eps)
%!assert (gpcdf (x, [0, 0, 0, NaN, 0, 0], 1, 0), [y1(1:3), NaN, y1(5:6)], eps)
%!assert (gpcdf (x, 0, [1, 1, 1, NaN, 1, 1], 0), [y1(1:3), NaN, y1(5:6)], eps)
%!assert (gpcdf (x, 0, 1, [0, 0, 0, NaN, 0, 0]), [y1(1:3), NaN, y1(5:6)], eps)
%!assert (gpcdf ([x(1:3), NaN, x(5:6)], 0, 1, 0), [y1(1:3), NaN, y1(5:6)], eps)
%!assert (gpcdf (x, zeros (1,6), ones (1,6), ones (1,6)), y2, eps)
%!assert (gpcdf (x, zeros (1,6), 1, 1), y2, eps)
%!assert (gpcdf (x, 0, ones (1,6), 1), y2, eps)
%!assert (gpcdf (x, 0, 1, ones (1,6)), y2, eps)
%!assert (gpcdf (x, 0, 1, 1), y2, eps)
%!assert (gpcdf (x, [0, 0, 0, NaN, 0, 0], 1, 1), [y2(1:3), NaN, y2(5:6)], eps)
%!assert (gpcdf (x, 0, [1, 1, 1, NaN, 1, 1], 1), [y2(1:3), NaN, y2(5:6)], eps)
%!assert (gpcdf (x, 0, 1, [1, 1, 1, NaN, 1, 1]), [y2(1:3), NaN, y2(5:6)], eps)
%!assert (gpcdf ([x(1:3), NaN, x(5:6)], 0, 1, 1), [y2(1:3), NaN, y2(5:6)], eps)
%!assert (gpcdf (x, zeros (1,6), ones (1,6), -ones (1,6)), y3, eps)
%!assert (gpcdf (x, zeros (1,6), 1, -1), y3, eps)
%!assert (gpcdf (x, 0, ones (1,6), -1), y3, eps)
%!assert (gpcdf (x, 0, 1, -ones (1,6)), y3, eps)
%!assert (gpcdf (x, 0, 1, -1), y3, eps)
%!assert (gpcdf (x, [0, 0, 0, NaN, 0, 0], 1, -1), [y1(1:3), NaN, y3(5:6)], eps)
%!assert (gpcdf (x, 0, [1, 1, 1, NaN, 1, 1], -1), [y1(1:3), NaN, y3(5:6)], eps)
%!assert (gpcdf (x, 0, 1, [-1, -1, -1, NaN, -1, -1]), [y1(1:3), NaN, y3(5:6)], eps)
%!assert (gpcdf ([x(1:3), NaN, x(5:6)], 0, 1, -1), [y1(1:3), NaN, y3(5:6)], eps)
## Test class of input preserved
%!assert (gpcdf (single ([x, NaN]), 0, 1, 0), single ([y1, NaN]), eps('single'))
%!assert (gpcdf ([x, NaN], single (0), 1, 0), single ([y1, NaN]), eps('single'))
%!assert (gpcdf ([x, NaN], 0, single (1), 0), single ([y1, NaN]), eps('single'))
%!assert (gpcdf ([x, NaN], 0, 1, single (0)), single ([y1, NaN]), eps('single'))
%!assert (gpcdf (single ([x, NaN]), 0, 1, 1), single ([y2, NaN]), eps('single'))
%!assert (gpcdf ([x, NaN], single (0), 1, 1), single ([y2, NaN]), eps('single'))
%!assert (gpcdf ([x, NaN], 0, single (1), 1), single ([y2, NaN]), eps('single'))
%!assert (gpcdf ([x, NaN], 0, 1, single (1)), single ([y2, NaN]), eps('single'))
%!assert (gpcdf (single ([x, NaN]), 0, 1, -1), single ([y3, NaN]), eps('single'))
%!assert (gpcdf ([x, NaN], single (0), 1, -1), single ([y3, NaN]), eps('single'))
%!assert (gpcdf ([x, NaN], 0, single (1), -1), single ([y3, NaN]), eps('single'))
%!assert (gpcdf ([x, NaN], 0, 1, single (-1)), single ([y3, NaN]), eps('single'))
## Test input validation
%!error gpcdf ()
%!error gpcdf (1)
%!error gpcdf (1,2)
%!error gpcdf (1,2,3)
%!error gpcdf (1,2,3,4,5)
%!error gpcdf (ones (3), ones (2), ones (2), ones (2))
%!error gpcdf (ones (2), ones (3), ones (2), ones (2))
%!error gpcdf (ones (2), ones (2), ones (3), ones (2))
%!error gpcdf (ones (2), ones (2), ones (2), ones (3))
%!error gpcdf (i, 2, 2, 2)
%!error gpcdf (2, i, 2, 2)
%!error gpcdf (2, 2, i, 2)
%!error gpcdf (2, 2, 2, i)
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