\Header{cum3}{Calculate Third Order Cumulants}
\keyword{math}{cum3}
\keyword{multivariate}{cum3}
\begin{Description}\relax
Calculates an estimate of the third cumulant, or skewness, of a vector. 
Also, if more than one vector is specified, a product-moment of order 3 is
estimated.
\end{Description}
\begin{Usage}
\begin{verbatim}
cum3(a, b=a, c=a, unbiased=TRUE)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{a}] A vector of observations.

\item[\code{b}] Another vector of observations,  if not supplied it is set to the value of \code{a}.
If supplied then it must be the same length as \code{a}.

\item[\code{c}] Another vector of observations,  if not supplied it is set to the value of \code{a}.
If supplied then it must be the same length as \code{a}.

\item[\code{unbiased}] A logical value indicating whether the unbiased estimator should be used.  

\end{ldescription}
\end{Arguments}
\begin{Details}\relax
The unbiased estimator uses a multiplier of \code{n/((n-1)*(n-2))} where \code{n} is
the sample size, if \code{unbiased} is \code{FALSE} then a multiplier of \code{1/n} is used.
This is multiplied by \code{sum((a-mean(a))*(b-mean(b))*(c-mean(c)))} to give the
required estimate.
\end{Details}
\begin{Value}
The required estimate.
\end{Value}

