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<TITLE>GNU Octave - Statistics</TITLE>
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<P><HR><P>
<H1><A NAME="SEC158" HREF="octave_toc.html#TOC158">Statistics</A></H1>
<P>
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}.
</P>
<P>
<DL>
<DT><U>Function File:</U> <B>mean</B> <I>(<VAR>x</VAR>)</I>
<DD><A NAME="IDX764"></A>
If <VAR>x</VAR> is a vector, compute the mean of the elements of <VAR>x</VAR>
</P>
<PRE>
mean (x) = SUM_i x(i) / N
</PRE>
<P>
If <VAR>x</VAR> is a matrix, compute the mean for each column and return them
in a row vector.
</DL>
</P>
<P>
<DL>
<DT><U>Function File:</U> <B>median</B> <I>(<VAR>x</VAR>)</I>
<DD><A NAME="IDX765"></A>
If <VAR>x</VAR> is a vector, compute the median value of the elements of
<VAR>x</VAR>.
</P>
<PRE>
x(ceil(N/2)), N odd
median(x) =
(x(N/2) + x((N/2)+1))/2, N even
</PRE>
<P>
If <VAR>x</VAR> is a matrix, compute the median value for each
column and return them in a row vector.
</DL>
</P>
<P>
<DL>
<DT><U>Function File:</U> <B>std</B> <I>(<VAR>x</VAR>)</I>
<DD><A NAME="IDX766"></A>
If <VAR>x</VAR> is a vector, compute the standard deviation of the elements
of <VAR>x</VAR>.
</P>
<PRE>
std (x) = sqrt (sumsq (x - mean (x)) / (n - 1))
</PRE>
<P>
If <VAR>x</VAR> is a matrix, compute the standard deviation for
each column and return them in a row vector.
</DL>
</P>
<P>
<DL>
<DT><U>Function File:</U> <B>cov</B> <I>(<VAR>x</VAR>, <VAR>y</VAR>)</I>
<DD><A NAME="IDX767"></A>
If each row of <VAR>x</VAR> and <VAR>y</VAR> is an observation and each column is
a variable, the (<VAR>i</VAR>,<VAR>j</VAR>)-th entry of
<CODE>cov (<VAR>x</VAR>, <VAR>y</VAR>)</CODE> is the covariance between the <VAR>i</VAR>-th
variable in <VAR>x</VAR> and the <VAR>j</VAR>-th variable in <VAR>y</VAR>. If called
with one argument, compute <CODE>cov (<VAR>x</VAR>, <VAR>x</VAR>)</CODE>.
</DL>
</P>
<P>
<DL>
<DT><U>Function File:</U> <B>corrcoef</B> <I>(<VAR>x</VAR>, <VAR>y</VAR>)</I>
<DD><A NAME="IDX768"></A>
If each row of <VAR>x</VAR> and <VAR>y</VAR> is an observation and each column is
a variable, the (<VAR>i</VAR>,<VAR>j</VAR>)-th entry of
<CODE>corrcoef (<VAR>x</VAR>, <VAR>y</VAR>)</CODE> is the correlation between the
<VAR>i</VAR>-th variable in <VAR>x</VAR> and the <VAR>j</VAR>-th variable in <VAR>y</VAR>.
If called with one argument, compute <CODE>corrcoef (<VAR>x</VAR>, <VAR>x</VAR>)</CODE>.
</DL>
</P>
<P>
<DL>
<DT><U>Function File:</U> <B>kurtosis</B> <I>(<VAR>x</VAR>)</I>
<DD><A NAME="IDX769"></A>
If <VAR>x</VAR> is a vector of length <VAR>N</VAR>, return the kurtosis
</P>
<PRE>
kurtosis (x) = N^(-1) std(x)^(-4) sum ((x - mean(x)).^4) - 3
</PRE>
<P>
of <VAR>x</VAR>. If <VAR>x</VAR> is a matrix, return the row vector containing
the kurtosis of each column.
</DL>
</P>
<P>
<DL>
<DT><U>Function File:</U> <B>mahalanobis</B> <I>(<VAR>x</VAR>, <VAR>y</VAR>)</I>
<DD><A NAME="IDX770"></A>
Return the Mahalanobis' D-square distance between the multivariate
samples <VAR>x</VAR> and <VAR>y</VAR>, which must have the same number of
components (columns), but may have a different number of observations
(rows).
</DL>
</P>
<P>
<DL>
<DT><U>Function File:</U> <B>skewness</B> <I>(<VAR>x</VAR>)</I>
<DD><A NAME="IDX771"></A>
If <VAR>x</VAR> is a vector of length <VAR>N</VAR>, return the skewness
</P>
<PRE>
skewness (x) = N^(-1) std(x)^(-3) sum ((x - mean(x)).^3)
</PRE>
<P>
of <VAR>x</VAR>. If <VAR>x</VAR> is a matrix, return the row vector containing
the skewness of each column.
</DL>
</P>
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