Given a multivariate random sample, this set of functions returns the joint cumulants of multivariate polykays in terms of joint cumulants of the multivariate population underlying the sample. Multivariate polykays are unbiased estimators with minimum variance of joint cumulant products. These estimators are usually indexed by a list of integer vectors: each vector corresponds to a joint cumulant. When this list reduces to a list of single integers, the multivariate polykay reduces to a univariate polykay. When this list reduces to a single integer vector, the multivariate polykay reduces to a multivariate k-statistic. When this list contains a single integer vector with only one element, the multivariate k-statistic reduces to a univariate k-statistic.