  The chain rule for derivatives of a function of a function is extended to a
function of a statistical functional, and applied to obtain approximations to
the cumulants, distribution and quantiles of functions of sample moments, and
so to obtain third order confidence intervals and estimates of reduced bias for
functions of moments. As an example we give the distribution of the
standardized skewness for a normal sample to magnitude $O(n^{-2})$, where $n$
is the sample size.
