update packages

[CreaPhase.git] / octave_packages / m / statistics / base / kurtosis.m

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+## Copyright (C) 1996-2012 John W. Eaton
+##
+## 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} {} kurtosis (@var{x})
+## @deftypefnx {Function File} {} kurtosis (@var{x}, @var{dim})
+## Compute the kurtosis of the elements of the vector @var{x}.
+## @tex
+## $$
+##  {\rm kurtosis} (x) = {1\over N \sigma^4} \sum_{i=1}^N (x_i-\bar{x})^4 - 3
+## $$
+## where $\bar{x}$ is the mean value of $x$.
+## @end tex
+## @ifnottex
+##
+## @example
+## kurtosis (x) = 1/N std(x)^(-4) sum ((x - mean(x)).^4) - 3
+## @end example
+##
+## @end ifnottex
+## If @var{x} is a matrix, return the kurtosis over the
+## first non-singleton dimension of the matrix.  If the optional
+## @var{dim} argument is given, operate along this dimension.
+##
+## Note: The definition of kurtosis above yields a kurtosis of zero for the
+## stdnormal distribution and is sometimes referred to as "excess kurtosis".
+## To calculate kurtosis without the normalization factor of @math{-3} use
+## @code{moment (@var{x}, 4, 'c') / std (@var{x})^4}.
+## @seealso{var, skewness, moment}
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Created: 29 July 1994
+## Adapted-By: jwe
+
+function retval = kurtosis (x, dim)
+
+  if (nargin != 1 && nargin != 2)
+    print_usage ();
+  endif
+
+  if (! (isnumeric (x) || islogical (x)))
+    error ("kurtosis: X must be a numeric vector or matrix");
+  endif
+
+  nd = ndims (x);
+  sz = size (x);
+  if (nargin != 2)
+    ## Find the first non-singleton dimension.
+    (dim = find (sz > 1, 1)) || (dim = 1);
+  else
+    if (!(isscalar (dim) && dim == fix (dim))
+        || !(1 <= dim && dim <= nd))
+      error ("kurtosis: DIM must be an integer and a valid dimension");
+    endif
+  endif
+
+  n = sz(dim);
+  sz(dim) = 1;
+  x = center (x, dim);  # center also promotes integer to double for next line
+  retval = zeros (sz, class (x));
+  s = std (x, [], dim);
+  idx = find (s > 0);
+  x = sum (x.^4, dim);
+  retval(idx) = x(idx) ./ (n * s(idx) .^ 4) - 3;
+
+endfunction
+
+
+%!test
+%! x = [-1; 0; 0; 0; 1];
+%! y = [x, 2*x];
+%! assert (kurtosis (y), [-1.4, -1.4], sqrt (eps));
+
+%!assert (kurtosis (single(1)), single(0));
+
+%% Test input validation
+%!error kurtosis ()
+%!error kurtosis (1, 2, 3)
+%!error kurtosis (['A'; 'B'])
+%!error kurtosis (1, ones(2,2))
+%!error kurtosis (1, 1.5)
+%!error kurtosis (1, 0)
+%!error kurtosis (1, 3)
+