Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / statistics-1.1.3 / jsupdf.m

diff --git a/octave_packages/statistics-1.1.3/jsupdf.m b/octave_packages/statistics-1.1.3/jsupdf.m
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+## Copyright (C) 2006 Frederick (Rick) A Niles <niles@rickniles.com>
+##
+## 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; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} jsupdf (@var{x}, @var{alpha1}, @var{alpha2})
+## For each element of @var{x}, compute the probability density function
+## (PDF) at @var{x} of the Johnson SU distribution with shape parameters @var{alpha1}
+## and @var{alpha2}.
+##
+## Default values are @var{alpha1} = 1, @var{alpha2} = 1.
+## @end deftypefn
+
+## Author: Frederick (Rick) A Niles <niles@rickniles.com>
+## Description: PDF of Johnson SU distribution
+
+## This function is derived from normpdf.m
+
+## This is the TeX equation of this function:
+##
+## \[ f(x) = \frac{\alpha_2}{\sqrt{x^2+1}} \phi\left(\alpha_1+\alpha_2
+## \log{\left(x+\sqrt{x^2+1}\right)}\right) \]
+##
+## where \[ -\infty < x < \infty ; \alpha_2 > 0 \] and $\phi$ is the
+## standard normal probability distribution function.  $\alpha_1$ and
+## $\alpha_2$ are shape parameters.
+
+function pdf = jsupdf (x, alpha1, alpha2)
+
+  if (nargin != 1 && nargin != 3)
+    print_usage;
+  endif
+
+  if (nargin == 1)
+    alpha1 = 1;
+    alpha2 = 1;
+  endif
+
+  if (!isscalar (alpha1) || !isscalar(alpha2))
+    [retval, x, alpha1, alpha2] = common_size (x, alpha1, alpha2);
+    if (retval > 0)
+      error ("normpdf: x, alpha1 and alpha2 must be of common size or scalars");
+    endif
+  endif
+
+  one = ones(size(x));
+  sr = sqrt(x.*x + one);
+  pdf = (alpha2 ./ sr) .* stdnormal_pdf (alpha1 .* one +
+                                         alpha2 .* log (x + sr));
+
+endfunction