update packages

[CreaPhase.git] / octave_packages / m / statistics / tests / z_test.m

diff --git a/octave_packages/m/statistics/tests/z_test.m b/octave_packages/m/statistics/tests/z_test.m
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+## Copyright (C) 1995-2012 Kurt Hornik
+##
+## 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} {[@var{pval}, @var{z}] =} z_test (@var{x}, @var{m}, @var{v}, @var{alt})
+## Perform a Z-test of the null hypothesis @code{mean (@var{x}) ==
+## @var{m}} for a sample @var{x} from a normal distribution with unknown
+## mean and known variance @var{v}.  Under the null, the test statistic
+## @var{z} follows a standard normal distribution.
+##
+## With the optional argument string @var{alt}, the alternative of
+## interest can be selected.  If @var{alt} is @code{"!="} or
+## @code{"<>"}, the null is tested against the two-sided alternative
+## @code{mean (@var{x}) != @var{m}}.  If @var{alt} is @code{">"}, the
+## one-sided alternative @code{mean (@var{x}) > @var{m}} is considered.
+## Similarly for @code{"<"}, the one-sided alternative @code{mean
+## (@var{x}) < @var{m}} is considered.  The default is the two-sided
+## case.
+##
+## The p-value of the test is returned in @var{pval}.
+##
+## If no output argument is given, the p-value of the test is displayed
+## along with some information.
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Description: Test for mean of a normal sample with known variance
+
+function [pval, z] = z_test (x, m, v, alt)
+
+  if ((nargin < 3) || (nargin > 4))
+    print_usage ();
+  endif
+
+  if (! isvector (x))
+    error ("z_test: X must be a vector");
+  endif
+  if (! isscalar (m))
+    error ("z_test: M must be a scalar");
+  endif
+  if (! (isscalar (v) && (v > 0)))
+    error ("z_test: V must be a positive scalar");
+  endif
+
+  n = length (x);
+  z = sqrt (n/v) * (sum (x) / n - m);
+  cdf = stdnormal_cdf (z);
+
+  if (nargin == 3)
+    alt = "!=";
+  endif
+
+  if (! ischar (alt))
+    error ("z_test: ALT must be a string");
+  elseif (strcmp (alt, "!=") || strcmp (alt, "<>"))
+    pval = 2 * min (cdf, 1 - cdf);
+  elseif (strcmp (alt, ">"))
+    pval = 1 - cdf;
+  elseif (strcmp (alt, "<"))
+    pval = cdf;
+  else
+    error ("z_test: option %s not recognized", alt);
+  endif
+
+  if (nargout == 0)
+    s = cstrcat ("Z-test of mean(x) == %g against mean(x) %s %g,\n",
+                "with known var(x) == %g:\n",
+                "  pval = %g\n");
+    printf (s, m, alt, m, v, pval);
+  endif
+
+endfunction