1 ## Copyright (C) 2012 Rik Wehbring
2 ## Copyright (C) 1995-2012 Kurt Hornik
4 ## This file is part of Octave.
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7 ## under the terms of the GNU General Public License as published by
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21 ## @deftypefn {Function File} {} cauchy_pdf (@var{x})
22 ## @deftypefnx {Function File} {} cauchy_pdf (@var{x}, @var{location}, @var{scale})
23 ## For each element of @var{x}, compute the probability density function
24 ## (PDF) at @var{x} of the Cauchy distribution with location parameter
25 ## @var{location} and scale parameter @var{scale} > 0. Default values are
26 ## @var{location} = 0, @var{scale} = 1.
29 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
30 ## Description: PDF of the Cauchy distribution
32 function pdf = cauchy_pdf (x, location = 0, scale = 1)
34 if (nargin != 1 && nargin != 3)
38 if (!isscalar (location) || !isscalar (scale))
39 [retval, x, location, scale] = common_size (x, location, scale);
41 error ("cauchy_pdf: X, LOCATION, and SCALE must be of common size or scalars");
45 if (iscomplex (x) || iscomplex (location) || iscomplex (scale))
46 error ("cauchy_pdf: X, LOCATION, and SCALE must not be complex");
49 if (isa (x, "single") || isa (location, "single") || isa (scale, "single"))
50 pdf = NaN (size (x), "single");
55 k = !isinf (location) & (scale > 0) & (scale < Inf);
56 if (isscalar (location) && isscalar (scale))
57 pdf = ((1 ./ (1 + ((x - location) / scale) .^ 2))
60 pdf(k) = ((1 ./ (1 + ((x(k) - location(k)) ./ scale(k)) .^ 2))
68 %! x = [-1 0 0.5 1 2];
69 %! y = 1/pi * ( 2 ./ ((x-1).^2 + 2^2) );
70 %!assert(cauchy_pdf (x, ones(1,5), 2*ones(1,5)), y);
71 %!assert(cauchy_pdf (x, 1, 2*ones(1,5)), y);
72 %!assert(cauchy_pdf (x, ones(1,5), 2), y);
73 %!assert(cauchy_pdf (x, [-Inf 1 NaN 1 Inf], 2), [NaN y(2) NaN y(4) NaN]);
74 %!assert(cauchy_pdf (x, 1, 2*[0 1 NaN 1 Inf]), [NaN y(2) NaN y(4) NaN]);
75 %!assert(cauchy_pdf ([x, NaN], 1, 2), [y, NaN]);
77 %% Test class of input preserved
78 %!assert(cauchy_pdf (single([x, NaN]), 1, 2), single([y, NaN]), eps("single"));
79 %!assert(cauchy_pdf ([x, NaN], single(1), 2), single([y, NaN]), eps("single"));
80 %!assert(cauchy_pdf ([x, NaN], 1, single(2)), single([y, NaN]), eps("single"));
82 %% Cauchy (0,1) == Student's T distribution with 1 DOF
85 %! assert(cauchy_pdf (x, 0, 1), tpdf (x, 1), eps);
87 %% Test input validation
89 %!error cauchy_pdf (1,2)
90 %!error cauchy_pdf (1,2,3,4)
91 %!error cauchy_pdf (ones(3),ones(2),ones(2))
92 %!error cauchy_pdf (ones(2),ones(3),ones(2))
93 %!error cauchy_pdf (ones(2),ones(2),ones(3))
94 %!error cauchy_pdf (i, 2, 2)
95 %!error cauchy_pdf (2, i, 2)
96 %!error cauchy_pdf (2, 2, i)