  kStatistics is a package in R that serves as a unified framework for
estimating univariate and multivariate cumulants as well as products of
univariate and multivariate cumulants of a random sample, using unbiased
estimators with minimum variance. The main computational machinery of
kStatistics is an algorithm for computing multi-index partitions. The same
algorithm underlies the general-purpose multivariate Fa\`a di Bruno's formula,
which has been therefore included in the last release of the package. This
formula gives the coefficients of formal power series compositions as well as
the partial derivatives of multivariable function compositions. One of the most
significant applications of this formula is the possibility to generate many
well-known polynomial families as special cases. So, in the package, there are
special functions for generating very popular polynomial families, such as the
Bell polynomials. However further families can be obtained, for suitable
choices of the formal power series involved in the composition or when suitable
symbolic strategies are employed. In both cases, we give examples on how to
modify the R codes of the package to accomplish this task. Future developments
are addressed at the end of the paper.
