Exact Distributions of Some Functions of the Ordered Multinomial Counts // Implements exact algorithms for computing the distributions of the maximum, the minimum, the range, and the sum of the J largest order statistics of a multinomial random vector. Two complementary algorithm families are provided: the recursive tree-traversal method of Bonetti, Cirillo, and Ogay (2019) doi:10.1098/rsos.190198, which covers all four statistics under the equiprobable hypothesis; and the stochastic matrix method of Corrado (2011) doi:10.1007/s11222-010-9174-3, which handles the maximum, minimum, and range for arbitrary probability vectors. Functions for power evaluation and sample size determination for goodness-of-fit tests based on these order statistics are also provided. Computationally intensive routines are implemented in 'C++' for efficiency.