Mercurial > octave-nkf
view scripts/statistics/distributions/betapdf.m @ 14138:72c96de7a403 stable
maint: update copyright notices for 2012
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Mon, 02 Jan 2012 14:25:41 -0500 |
parents | 19b9f17d22af |
children | f3d52523cde1 |
line wrap: on
line source
## 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)