octave-nkf: scripts/statistics/distributions/betapdf.m annotate

annotate scripts/statistics/distributions/betapdf.m @ 20644:4e307c55a2b5

Use isempty () rather than any () for faster code in inverse statistical distributions. betainv.m, binoinv.m, gaminv.m, poissinv.m: Use '! isempty (k)' rather than 'any (k)' for faster code.

author	Rik <rik@octave.org>
date	Sun, 11 Oct 2015 21:09:41 -0700
parents	9fc020886ae9
children

rev	line source
14138 72c96de7a403 maint: update copyright notices for 2012 John W. Eaton <jwe@octave.org> parents: 13171 diff changeset	1 ## Copyright (C) 2012 Rik Wehbring
19731 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 19309 diff changeset	2 ## Copyright (C) 1995-2015 Kurt Hornik
11269 628b03328765 improve range of betapdf function Christos Dimitrakakis <christos.dimitrakakis@gmail.com> parents: 10549 diff changeset	3 ## Copyright (C) 2010 Christos Dimitrakakis
5410 56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	4 ##
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	5 ## This file is part of Octave.
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	6 ##
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	7 ## Octave is free software; you can redistribute it and/or modify it
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	8 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	9 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	10 ## your option) any later version.
5410 56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	11 ##
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	12 ## Octave is distributed in the hope that it will be useful, but
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	13 ## WITHOUT ANY WARRANTY; without even the implied warranty of
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	14 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	15 ## General Public License for more details.
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	16 ##
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	17 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	18 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	19 ## <http://www.gnu.org/licenses/>.
5410 56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	20
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	21 ## -- texinfo --
5411 bee21f388110 [project @ 2005-07-13 17:53:44 by jwe] jwe parents: 5410 diff changeset	22 ## @deftypefn {Function File} {} betapdf (@var{x}, @var{a}, @var{b})
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	23 ## For each element of @var{x}, compute the probability density function (PDF)
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	24 ## at @var{x} of the Beta distribution with parameters @var{a} and @var{b}.
5410 56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	25 ## @end deftypefn
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	26
11269 628b03328765 improve range of betapdf function Christos Dimitrakakis <christos.dimitrakakis@gmail.com> parents: 10549 diff changeset	27 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>, CD <christos.dimitrakakis@gmail.com>
5410 56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	28 ## Description: PDF of the Beta distribution
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	29
5411 bee21f388110 [project @ 2005-07-13 17:53:44 by jwe] jwe parents: 5410 diff changeset	30 function pdf = betapdf (x, a, b)
5410 56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	31
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	32 if (nargin != 3)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5428 diff changeset	33 print_usage ();
5410 56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	34 endif
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	35
19867 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19731 diff changeset	36 if (! isscalar (a) \|\| ! isscalar (b))
5410 56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	37 [retval, x, a, b] = common_size (x, a, b);
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	38 if (retval > 0)
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	39 error ("betapdf: X, A, and B must be of common size or scalars");
5410 56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	40 endif
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	41 endif
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	42
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	43 if (iscomplex (x) \|\| iscomplex (a) \|\| iscomplex (b))
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	44 error ("betapdf: X, A, and B must not be complex");
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	45 endif
5410 56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	46
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	47 if (isa (x, "single") \|\| isa (a, "single") \|\| isa (b, "single"));
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	48 pdf = zeros (size (x), "single");
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	49 else
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	50 pdf = zeros (size (x));
5410 56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	51 endif
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	52
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	53 k = !(a > 0) \| !(b > 0) \| isnan (x);
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	54 pdf(k) = NaN;
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	55
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	56 k = (x > 0) & (x < 1) & (a > 0) & (b > 0) & ((a != 1) \| (b != 1));
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	57 if (isscalar (a) && isscalar (b))
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	58 pdf(k) = exp ((a - 1) * log (x(k))
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	59 + (b - 1) * log (1 - x(k))
19309 653ed3a6ba83 Use gammaln in preference to lgamma in core Octave code. Rik <rik@octave.org> parents: 17744 diff changeset	60 + gammaln (a + b) - gammaln (a) - gammaln (b));
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	61 else
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	62 pdf(k) = exp ((a(k) - 1) .* log (x(k))
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	63 + (b(k) - 1) .* log (1 - x(k))
19309 653ed3a6ba83 Use gammaln in preference to lgamma in core Octave code. Rik <rik@octave.org> parents: 17744 diff changeset	64 + gammaln (a(k) + b(k)) - gammaln (a(k)) - gammaln (b(k)));
11269 628b03328765 improve range of betapdf function Christos Dimitrakakis <christos.dimitrakakis@gmail.com> parents: 10549 diff changeset	65 endif
628b03328765 improve range of betapdf function Christos Dimitrakakis <christos.dimitrakakis@gmail.com> parents: 10549 diff changeset	66
628b03328765 improve range of betapdf function Christos Dimitrakakis <christos.dimitrakakis@gmail.com> parents: 10549 diff changeset	67 ## Most important special cases when the density is finite.
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	68 k = (x == 0) & (a == 1) & (b > 0) & (b != 1);
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	69 if (isscalar (a) && isscalar (b))
19309 653ed3a6ba83 Use gammaln in preference to lgamma in core Octave code. Rik <rik@octave.org> parents: 17744 diff changeset	70 pdf(k) = exp (gammaln (a + b) - gammaln (a) - gammaln (b));
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	71 else
19309 653ed3a6ba83 Use gammaln in preference to lgamma in core Octave code. Rik <rik@octave.org> parents: 17744 diff changeset	72 pdf(k) = exp (gammaln (a(k) + b(k)) - gammaln (a(k)) - gammaln (b(k)));
5410 56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	73 endif
56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	74
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	75 k = (x == 1) & (b == 1) & (a > 0) & (a != 1);
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	76 if (isscalar (a) && isscalar (b))
19309 653ed3a6ba83 Use gammaln in preference to lgamma in core Octave code. Rik <rik@octave.org> parents: 17744 diff changeset	77 pdf(k) = exp (gammaln (a + b) - gammaln (a) - gammaln (b));
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	78 else
19309 653ed3a6ba83 Use gammaln in preference to lgamma in core Octave code. Rik <rik@octave.org> parents: 17744 diff changeset	79 pdf(k) = exp (gammaln (a(k) + b(k)) - gammaln (a(k)) - gammaln (b(k)));
11269 628b03328765 improve range of betapdf function Christos Dimitrakakis <christos.dimitrakakis@gmail.com> parents: 10549 diff changeset	80 endif
628b03328765 improve range of betapdf function Christos Dimitrakakis <christos.dimitrakakis@gmail.com> parents: 10549 diff changeset	81
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	82 k = (x >= 0) & (x <= 1) & (a == 1) & (b == 1);
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	83 pdf(k) = 1;
11269 628b03328765 improve range of betapdf function Christos Dimitrakakis <christos.dimitrakakis@gmail.com> parents: 10549 diff changeset	84
628b03328765 improve range of betapdf function Christos Dimitrakakis <christos.dimitrakakis@gmail.com> parents: 10549 diff changeset	85 ## Other special case when the density at the boundary is infinite.
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	86 k = (x == 0) & (a < 1);
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	87 pdf(k) = Inf;
11269 628b03328765 improve range of betapdf function Christos Dimitrakakis <christos.dimitrakakis@gmail.com> parents: 10549 diff changeset	88
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	89 k = (x == 1) & (b < 1);
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	90 pdf(k) = Inf;
11269 628b03328765 improve range of betapdf function Christos Dimitrakakis <christos.dimitrakakis@gmail.com> parents: 10549 diff changeset	91
5410 56e066f5efc1 [project @ 2005-07-13 17:43:35 by jwe] jwe parents: diff changeset	92 endfunction
11355 34c5cd5a17ec betapdf.m: Add test for large values of alpha and beta. Rik <octave@nomad.inbox5.com> parents: 11269 diff changeset	93
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	94
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	95 %!shared x,y
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	96 %! x = [-1 0 0.5 1 2];
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	97 %! y = [0 2 1 0 0];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	98 %!assert (betapdf (x, ones (1,5), 2*ones (1,5)), y)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	99 %!assert (betapdf (x, 1, 2*ones (1,5)), y)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	100 %!assert (betapdf (x, ones (1,5), 2), y)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	101 %!assert (betapdf (x, [0 NaN 1 1 1], 2), [NaN NaN y(3:5)])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	102 %!assert (betapdf (x, 1, 2*[0 NaN 1 1 1]), [NaN NaN y(3:5)])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	103 %!assert (betapdf ([x, NaN], 1, 2), [y, NaN])
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	104
19867 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19731 diff changeset	105 ## Test class of input preserved
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	106 %!assert (betapdf (single ([x, NaN]), 1, 2), single ([y, NaN]))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	107 %!assert (betapdf ([x, NaN], single (1), 2), single ([y, NaN]))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	108 %!assert (betapdf ([x, NaN], 1, single (2)), single ([y, NaN]))
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	109
19867 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19731 diff changeset	110 ## Beta (1/2,1/2) == arcsine distribution
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	111 %!test
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	112 %! x = rand (10,1);
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	113 %! y = 1./(pi * sqrt (x.*(1-x)));
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	114 %! assert (betapdf (x, 1/2, 1/2), y, 50*eps);
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	115
19867 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19731 diff changeset	116 ## Test large input values to betapdf
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	117 %!assert (betapdf (0.5, 1000, 1000), 35.678, 1e-3)
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	118
19867 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19731 diff changeset	119 ## Test input validation
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	120 %!error betapdf ()
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	121 %!error betapdf (1)
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	122 %!error betapdf (1,2)
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	123 %!error betapdf (1,2,3,4)
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	124 %!error betapdf (ones (3), ones (2), ones (2))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	125 %!error betapdf (ones (2), ones (3), ones (2))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	126 %!error betapdf (ones (2), ones (2), ones (3))
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	127 %!error betapdf (i, 2, 2)
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	128 %!error betapdf (2, i, 2)
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	129 %!error betapdf (2, 2, i)
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	130

Mercurial > octave-nkf

annotate scripts/statistics/distributions/betapdf.m @ 20644:4e307c55a2b5