3 papers
math.PR2026
A Unified Exact Factorial-Moment Theory for Multi-set Allocation Occupancy (MAO) in Finite Populations
Xing-gang Mao, Xiao-yan Xue
Let be independent uniformly selected subsets of a finite population of size , with prescribed cardinalities . For each population element, defi…
math.PR2026
Second-Order Multi-Set Allocation Occupancy (MAO) Distributions under Pairwise-Intersection Constraints: Exact Laws, MAO Norms, Inequalities, and Limit Theory
Xing-gang Mao
Our previous work established the multi-set allocation occupancy (MAO) distribution theory, including the norms, inequalities, and limit theory, under constraints on set sizes alon…
math.PR2025
The Multi-set Allocation Occupancy function and inequality (MAO function and MAO inequality): the foundation of Generalized hypergeometric distribution theory
Xing-gang Mao, Xiao-yan Xue
In our previous work, we studied the Generalized Hypergeometric Distribution (GHGD), which we refer to as the Multi-set Allocation Occupancy (MAO) distribution. We derived formulas…