@c Copyright (C) 1996 John W. Eaton
@c This is part of the Octave manual.
@c For copying conditions, see the file gpl.texi.

@node Statistics, Plotting, Sets, Top
@chapter Statistics

I hope that someday Octave will include more statistics functions.  If
you would like to help improve Octave in this area, please contact
@code{bug-octave@@bevo.che.wisc.edu}.

@ftable @code
@item corrcoef (@var{x} [, @var{y}])
If each row of @var{x} and @var{y} is an observation and each column is
a variable, the (@var{i},@var{j})-th entry of
@code{corrcoef (@var{x}, @var{y})} is the correlation between the
@var{i}-th variable in @var{x} and the @var{j}-th variable in @var{y}.
If invoked with one argument, compute @code{corrcoef (@var{x}, @var{x})}.

@item cov (@var{x} [, @var{y}])
If each row of @var{x} and @var{y} is an observation and each column is
a variable, the (@var{i},@var{j})-th entry of
@code{cov (@var{x}, @var{y})} is the covariance between the @var{i}-th
variable in @var{x} and the @var{j}-th variable in @var{y}.  If invoked
with one argument, compute @code{cov (@var{x}, @var{x})}.

@item kurtosis (@var{x})
If @var{x} is a vector of length @var{N}, return the kurtosis

@example
kurtosis(x) = N^(-1) std(x)^(-4) SUM_i (x(i)-mean(x))^4 - 3
@end example

@noindent
of @var{x}.  If @var{x} is a matrix, return the row vector containing
the kurtosis of each column.

@item mahalanobis (@var{x}, @var{y})
Returns Mahalanobis' D-square distance between the multivariate samples
@var{x} and @var{y}, which must have the same number of components
(columns), but may have a different number of observations (rows).

@item mean (@var{a})
If @var{a} is a vector, compute the mean of the elements of @var{a}.  If
@var{a} is a matrix, compute the mean for each column and return them in
a row vector.

@item median (@var{a})
If @var{a} is a vector, compute the median value of the elements of
@var{a}.  If @var{a} is a matrix, compute the median value for each
column and return them in a row vector.

@item skewness (@var{x})
If @var{x} is a vector of length @var{N}, return the skewness

@example
skewness (x) = N^(-1) std(x)^(-3) SUM_i (x(i)-mean(x))^3
@end example

@noindent
of @var{x}.  If @var{x} is a matrix, return the row vector containing
the skewness of each column.

@item std (@var{a})
If @var{a} is a vector, compute the standard deviation of the elements
of @var{a}.  If @var{a} is a matrix, compute the standard deviation for
each column and return them in a row vector.
@end ftable