--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/doc/interpreter/stats.txi	Tue Oct 19 10:08:42 1999 +0000
@@ -0,0 +1,140 @@
+@c Copyright (C) 1996, 1997 John W. Eaton
+@c This is part of the Octave manual.
+@c For copying conditions, see the file gpl.texi.
+
+@node Statistics, Sets, Optimization, 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
+@email{bug-octave@@bevo.che.wisc.edu}.
+
+@deftypefn {Function File} {} mean (@var{x})
+If @var{x} is a vector, compute the mean of the elements of @var{x}
+@iftex
+@tex
+$$ {\rm mean}(x) = \bar{x} = {1\over N} \sum_{i=1}^N x_i $$
+@end tex
+@end iftex
+@ifinfo
+
+@example
+mean (x) = SUM_i x(i) / N
+@end example
+@end ifinfo
+If @var{x} is a matrix, compute the mean for each column and return them
+in a row vector.
+@end deftypefn
+
+@deftypefn {Function File} {} median (@var{x})
+If @var{x} is a vector, compute the median value of the elements of
+@var{x}.
+@iftex
+@tex
+$$
+{\rm median} (x) =
+  \cases{x(\lceil N/2\rceil), & $N$ odd;\cr
+          (x(N/2)+x(N/2+1))/2, & $N$ even.}
+$$
+@end tex
+@end iftex
+@ifinfo
+
+@example
+@group
+            x(ceil(N/2)),             N odd
+median(x) = 
+            (x(N/2) + x((N/2)+1))/2,  N even
+@end group
+@end example
+@end ifinfo
+If @var{x} is a matrix, compute the median value for each
+column and return them in a row vector.
+@end deftypefn
+
+@deftypefn {Function File} {} std (@var{x})
+If @var{x} is a vector, compute the standard deviation of the elements
+of @var{x}.
+@iftex
+@tex
+$$
+{\rm std} (x) = \sigma (x) = \sqrt{{\sum_{i=1}^N (x_i - \bar{x}) \over N - 1}}
+$$
+@end tex
+@end iftex
+@ifinfo
+
+@example
+@group
+std (x) = sqrt (sumsq (x - mean (x)) / (n - 1))
+@end group
+@end example
+@end ifinfo
+If @var{x} is a matrix, compute the standard deviation for
+each column and return them in a row vector.
+@end deftypefn
+
+@deftypefn {Function File} {} 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 called
+with one argument, compute @code{cov (@var{x}, @var{x})}.
+@end deftypefn
+
+@deftypefn {Function File} {} 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 called with one argument, compute @code{corrcoef (@var{x}, @var{x})}.
+@end deftypefn
+
+@deftypefn {Function File} {} kurtosis (@var{x})
+If @var{x} is a vector of length @var{N}, return the kurtosis
+@iftex
+@tex
+$$
+ {\rm kurtosis} (x) = {1\over N \sigma(x)^4} \sum_{i=1}^N (x_i-\bar{x})^4 - 3
+$$
+@end tex
+@end iftex
+@ifinfo
+
+@example
+kurtosis (x) = N^(-1) std(x)^(-4) sum ((x - mean(x)).^4) - 3
+@end example
+@end ifinfo
+
+@noindent
+of @var{x}.  If @var{x} is a matrix, return the row vector containing
+the kurtosis of each column.
+@end deftypefn
+
+@deftypefn {Function File} {} mahalanobis (@var{x}, @var{y})
+Return the 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).
+@end deftypefn
+
+@deftypefn {Function File} {} skewness (@var{x})
+If @var{x} is a vector of length @var{N}, return the skewness
+@iftex
+@tex
+$$
+{\rm skewness} (x) = {1\over N \sigma(x)^3} \sum_{i=1}^N (x_i-\bar{x})^3
+$$
+@end tex
+@end iftex
+@ifinfo
+
+@example
+skewness (x) = N^(-1) std(x)^(-3) sum ((x - mean(x)).^3)
+@end example
+@end ifinfo
+
+@noindent
+of @var{x}.  If @var{x} is a matrix, return the row vector containing
+the skewness of each column.
+@end deftypefn