Smallest covering regions and highest density regions for discrete distributions

Abstract This paper examines the problem of computing a canonical smallest covering region for an arbitrary discrete probability distribution. optimisation is similar to classical 0–1 knapsack problem, but it involves over set that may be countably infinite, raising computational challenge makes non-trivial. To solve we present theorems giving useful conditions optimising and develop iterative one-at-a-time method compute region. We show how this can programmed in pseudo-code examine performance our method. compare algorithm with other algorithms available statistical computation packages HDRs. find only one accurately computes HDRs distributions.