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math.PR2026
Absolute moments of the binomial distribution folded at its mean
Neven Elezović
Let and \(Y=|X-Np|\). We derive an exact reduction for every odd absolute moment of \(Y\), expressing it through finitely many central masses and central tail prob…
math.PR2026
Multinomial probabilities near the mode: integer modes and the complete local expansion
Neven Elezović
Let with and . We study for lattice points near from two complementary viewpoints. First, we give an exac…
math.PR2026
The mean absolute deviation of the classical discrete distributions: collapse identities, complete asymptotic expansions, and enveloping series
Neven Elezović
For each of the four classical discrete laws --- binomial, Poisson, negative binomial and hypergeometric --- the mean absolute deviation about the mean collapses to a single point…
stat.ME2026
Comb Test: Histogram Uniformity Testing Based on Discrete Total Variation
Nikola Banić, Neven Elezović
Histogram uniformity testing is a common statistical task usually performed using Pearson's chi-square test. This paper proposes a complementary test based on the discrete total va…