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>

A simulation study is carried out in order to compare the performance of the Lincoln-Petersen and Chapman estimators for single capture-recapture or dual system estimation when the sizes of the samples or record systems are not fixed by the researcher. Performance is explored through both bias...