update packages

[CreaPhase.git] / octave_packages / m / statistics / distributions / betapdf.m

diff --git a/octave_packages/m/statistics/distributions/betapdf.m b/octave_packages/m/statistics/distributions/betapdf.m
new file mode 100644 (file)
index 0000000..17d35ca
--- /dev/null
+++ b/octave_packages/m/statistics/distributions/betapdf.m
@@ -0,0 +1,130 @@
+## Copyright (C) 2012 Rik Wehbring
+## Copyright (C) 1995-2012 Kurt Hornik
+## Copyright (C) 2010 Christos Dimitrakakis
+##
+## 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 {Function File} {} betapdf (@var{x}, @var{a}, @var{b})
+## For each element of @var{x}, compute the probability density function (PDF)
+## at @var{x} of the Beta distribution with parameters @var{a} and @var{b}.
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>, CD <christos.dimitrakakis@gmail.com>
+## Description: PDF of the Beta distribution
+
+function pdf = betapdf (x, a, b)
+
+  if (nargin != 3)
+    print_usage ();
+  endif
+
+  if (!isscalar (a) || !isscalar (b))
+    [retval, x, a, b] = common_size (x, a, b);
+    if (retval > 0)
+      error ("betapdf: X, A, and B must be of common size or scalars");
+    endif
+  endif
+
+  if (iscomplex (x) || iscomplex (a) || iscomplex (b))
+    error ("betapdf: X, A, and B must not be complex");
+  endif
+
+  if (isa (x, "single") || isa (a, "single") || isa (b, "single"));
+    pdf = zeros (size (x), "single");
+  else
+    pdf = zeros (size (x));
+  endif
+
+  k = !(a > 0) | !(b > 0) | isnan (x);
+  pdf(k) = NaN;
+
+  k = (x > 0) & (x < 1) & (a > 0) & (b > 0) & ((a != 1) | (b != 1));
+  if (isscalar (a) && isscalar (b))
+    pdf(k) = exp ((a - 1) * log (x(k))
+                  + (b - 1) * log (1 - x(k))
+                  + lgamma (a + b) - lgamma (a) - lgamma (b));
+  else
+    pdf(k) = exp ((a(k) - 1) .* log (x(k))
+                  + (b(k) - 1) .* log (1 - x(k))
+                  + lgamma (a(k) + b(k)) - lgamma (a(k)) - lgamma (b(k)));
+  endif
+
+  ## Most important special cases when the density is finite.
+  k = (x == 0) & (a == 1) & (b > 0) & (b != 1);
+  if (isscalar (a) && isscalar (b))
+    pdf(k) = exp (lgamma (a + b) - lgamma (a) - lgamma (b));
+  else
+    pdf(k) = exp (lgamma (a(k) + b(k)) - lgamma (a(k)) - lgamma (b(k)));
+  endif
+
+  k = (x == 1) & (b == 1) & (a > 0) & (a != 1);
+  if (isscalar (a) && isscalar (b))
+    pdf(k) = exp (lgamma (a + b) - lgamma (a) - lgamma (b));
+  else
+    pdf(k) = exp (lgamma (a(k) + b(k)) - lgamma (a(k)) - lgamma (b(k)));
+  endif
+
+  k = (x >= 0) & (x <= 1) & (a == 1) & (b == 1);
+  pdf(k) = 1;
+
+  ## Other special case when the density at the boundary is infinite.
+  k = (x == 0) & (a < 1);
+  pdf(k) = Inf;
+
+  k = (x == 1) & (b < 1);
+  pdf(k) = Inf;
+
+endfunction
+
+
+%!shared x,y
+%! x = [-1 0 0.5 1 2];
+%! y = [0 2 1 0 0];
+%!assert(betapdf (x, ones(1,5), 2*ones(1,5)), y);
+%!assert(betapdf (x, 1, 2*ones(1,5)), y);
+%!assert(betapdf (x, ones(1,5), 2), y);
+%!assert(betapdf (x, [0 NaN 1 1 1], 2), [NaN NaN y(3:5)]);
+%!assert(betapdf (x, 1, 2*[0 NaN 1 1 1]), [NaN NaN y(3:5)]);
+%!assert(betapdf ([x, NaN], 1, 2), [y, NaN]);
+
+%% Test class of input preserved
+%!assert(betapdf (single([x, NaN]), 1, 2), single([y, NaN]));
+%!assert(betapdf ([x, NaN], single(1), 2), single([y, NaN]));
+%!assert(betapdf ([x, NaN], 1, single(2)), single([y, NaN]));
+
+%% Beta (1/2,1/2) == arcsine distribution
+%!test
+%! x = rand (10,1);
+%! y = 1./(pi * sqrt (x.*(1-x)));
+%! assert(betapdf (x, 1/2, 1/2), y, 50*eps);
+
+%% Test large input values to betapdf
+%!assert (betapdf(0.5, 1000, 1000), 35.678, 1e-3)
+
+%% Test input validation
+%!error betapdf ()
+%!error betapdf (1)
+%!error betapdf (1,2)
+%!error betapdf (1,2,3,4)
+%!error betapdf (ones(3),ones(2),ones(2))
+%!error betapdf (ones(2),ones(3),ones(2))
+%!error betapdf (ones(2),ones(2),ones(3))
+%!error betapdf (i, 2, 2)
+%!error betapdf (2, i, 2)
+%!error betapdf (2, 2, i)
+