In recent years, the actuarial literature involving machine learning in insurance pricing has flourished. However, most actuarial machine learning research focuses on property and casualty insurance, while using such techniques in health insurance is yet to be explored. In this paper, we discuss...

For the first time, explicit expressions are given for the cumulants of the multinomial and the negative multinomial distributions. These expressions are given in terms of Stirling numbers. Computational efficiency of the expressions is illustrated.

<Para ID="Par1">Contingency tables are often used to display the multivariate frequency distribution of variables of interest. Under the common multinomial assumption, the first step of contingency table analysis is to estimate cell probabilities. It is well known that the unconstrained maximum likelihood...</para>