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) , which covers all four statistics under the equiprobable hypothesis; and the stochastic matrix method of Corrado (2011) , 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.