## Copyright (C) 2022 Nicholas R. Jankowski ## Copyright (C) 2012 Rik Wehbring ## Copyright (C) 1996-2016 Kurt Hornik ## ## This program 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. ## ## This program 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 this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {@var{pdf} =} hygepdf (@var{x}, @var{t}, @var{m}, @var{n}) ## @deftypefnx {} {@var{pdf} =} hygepdf (@dots{}, "vectorexpand") ## Compute the probability density function (PDF) at @var{x} of the ## hypergeometric distribution with parameters @var{t}, @var{m}, and @var{n}. ## ## This is the probability of obtaining @var{x} marked items when randomly ## drawing a sample of size @var{n} without replacement from a population of ## total size @var{t} containing @var{m} marked items. ## ## The parameters @var{t}, @var{m}, and @var{n} must be positive integers ## with @var{m} and @var{n} not greater than @var{t}. They and @var{x} may be ## scalars or arrays, but all non-scalars must be the same size. ## ## The output @var{pdf} will be the same size as the input array. ## ## If the optional parameter @code{vectorexpand} is provided, @var{x} may be an ## array with size different from parameters @var{t}, @var{m}, and @var{n} ## (which must still be of a common size or scalar). Each element of @var{x} ## will be evaluated against each set of parameters @var{t}, @var{m}, and ## @var{n} in columnwise order. The output @var{pdf} will be an array of size ## @code{@var{r} x @var{s}}, where @code{@var{r} = numel (@var{t})}, and ## @code{@var{s} = numel (@var{x})}. ## ## @end deftypefn ## Author: KH ## Description: PDF of the hypergeometric distribution function pdf = hygepdf (x, t, m, n, vect_expand = "") if (!any (nargin == [4,5])) print_usage (); endif if (iscomplex (x) || iscomplex (t) || iscomplex (m) || iscomplex (n)) error ("hygepdf: X, T, M, and N must not be complex"); endif if strcmpi (vect_expand, "vectorexpand") ## Expansion to improve vectorization of hyge calling functions. ## Project inputs over a 2D array with x(:) as a row vector and t,m,n as ## a column vector. each pdf(i,j) is hygepdf(x(j), t(i), m(i), n(i)) ## Following expansion, remainder of algorithm processes as normal. if (! isscalar (t) || ! isscalar (m) || ! isscalar (n)) [retval, t, m, n] = common_size (t, m, n); if (retval > 0) error ("hygepdf: T, M, and N must be of common size or scalars"); endif ## ensure col vectors before expansion t = t(:); m = m(:); n = n(:); endif ## expand x,t,m,n to arrays of size numel(t) x numel(x) sz = [numel(t), numel(x)]; x = x(:)'; # ensure row vector before expansion x = x(ones (sz(1), 1), :); t = t(:, ones (sz(2), 1)); m = m(:, ones (sz(2), 1)); n = n(:, ones (sz(2), 1)); else if (! isscalar (t) || ! isscalar (m) || ! isscalar (n)) [retval, x, t, m, n] = common_size (x, t, m, n); if (retval > 0) error ("hygepdf: X, T, M, and N must be of common size or scalars"); endif endif sz = size (x); endif if (isa (x, "single") || isa (t, "single") || isa (m, "single") || isa (n, "single")) pdf = zeros (sz, "single"); else pdf = zeros (sz); endif ## everything in nel gives NaN nel = (isnan (x) | (t < 0) | (m < 0) | (n <= 0) | (m > t) | (n > t) | (t != fix (t)) | (m != fix (m)) | (n != fix (n))); ## everything in zel gives 0 unless in nel zel = ((x != fix (x)) | (x < 0) | (x > m) | (n < x) | (n-x > t-m)); pdf(nel) = NaN; k = ! nel & ! zel; if (any (k(:))) if (isscalar (t)) pdf(k) = exp (gammaln (m+1) - gammaln (m-x(k)+1) - gammaln (x(k)+1) +... gammaln (t-m+1) - gammaln (t-m-n+x(k)+1) - ... gammaln (n-x(k)+1) - gammaln (t+1) + gammaln (t-n+1) + ... gammaln (n+1)); else pdf(k) = exp (gammaln (m(k)+1) - gammaln (m(k)-x(k)+1) - ... gammaln (x(k)+1) + gammaln (t(k)-m(k)+1) - ... gammaln (t(k)-m(k)-n(k)+x(k)+1) - gammaln (n(k)-x(k)+1) - ... gammaln (t(k)+1) + gammaln (t(k)-n(k)+1) + gammaln (n(k)+1)); endif endif endfunction %!shared x,y %! x = [-1 0 1 2 3]; %! y = [0 1/6 4/6 1/6 0]; %!assert (hygepdf (x, 4*ones (1,5), 2, 2), y, eps) %!assert (hygepdf (x, 4, 2*ones (1,5), 2), y, eps) %!assert (hygepdf (x, 4, 2, 2*ones (1,5)), y, eps) %!assert (hygepdf (x, 4*[1 -1 NaN 1.1 1], 2, 2), [0 NaN NaN NaN 0], eps) %!assert (hygepdf (x, 4, 2*[1 -1 NaN 1.1 1], 2), [0 NaN NaN NaN 0], eps) %!assert (hygepdf (x, 4, 5, 2), [NaN NaN NaN NaN NaN], eps) %!assert (hygepdf (x, 4, 2, 2*[1 -1 NaN 1.1 1]), [0 NaN NaN NaN 0], eps) %!assert (hygepdf (x, 4, 2, 5), [NaN NaN NaN NaN NaN], eps) %!assert (hygepdf ([x, NaN], 4, 2, 2), [y, NaN], eps) ## Test class of input preserved %!assert (hygepdf (single ([x, NaN]), 4, 2, 2), single ([y, NaN]), eps("single")) %!assert (hygepdf ([x, NaN], single (4), 2, 2), single ([y, NaN]), eps("single")) %!assert (hygepdf ([x, NaN], 4, single (2), 2), single ([y, NaN]), eps("single")) %!assert (hygepdf ([x, NaN], 4, 2, single (2)), single ([y, NaN]), eps("single")) ## Test vector expansion %!test %! z = zeros(3,5); %! z([4,5,6,8,9,12]) = [1, 0.5, 1/6, 0.5, 2/3, 1/6]; %! assert (hygepdf (x, 4, [0 1 2], 2,"vectorexpand"), z, eps); %! assert (hygepdf (x, 4, [0 1 2]', 2,"vectorexpand"), z, eps); %! assert (hygepdf (x', 4, [0 1 2], 2,"vectorexpand"), z, eps); %! assert (hygepdf (2, 4, [0 1 2], 2,"vectorexpand"), z(:,4), eps); %! assert (hygepdf (x, 4, 1, 2,"vectorexpand"), z(2,:), eps); %! assert (hygepdf ([NaN,x], 4, [0 1 2]', 2,"vectorexpand"),[NaN(3,1), z], eps); ## Test input validation %!error hygepdf () %!error hygepdf (1) %!error hygepdf (1,2) %!error hygepdf (1,2,3) %!error hygepdf (1,2,3,4,5,6) %!error hygepdf (1, ones (3), ones (2), ones (2)) %!error hygepdf (1, ones (2), ones (3), ones (2)) %!error hygepdf (1, ones (2), ones (2), ones (3)) %!error hygepdf (i, 2, 2, 2) %!error hygepdf (2, i, 2, 2) %!error hygepdf (2, 2, i, 2) %!error hygepdf (2, 2, 2, i)