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9 papers
Discrete total variation under the multinomial, Part 3: expectation under a general distribution
Nikola Banić, Neven Elezović
For multinomial counts on ordered bins and a reference law we study the expectation of the reference-centered discrete total…
Discrete total variation under the multinomial, Part 2: variance under the uniform null
Nikola Banić, Neven Elezović
For the counts of observations in ordered bins we study the variance of the discrete total variation $d=\sum_{i=1}^{n-1}…
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…
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…
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…
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…
TVOR: Finding Discrete Total Variation Outliers among Histograms
Nikola Banić, Neven Elezović
Pearson's chi-squared test can detect outliers in the data distribution of a given set of histograms. However, in fields such as demographics (for e.g. birth years), outliers may b…
Asymptotic expansions of exponentials of digamma function and identity for Bernoulli polynomials
Neven Elezović
The asymptotic expansion of digamma function is a starting point for the derivation of approximants for harmonic sums or Euler-Mascheroni constant. It is usual to derive such appro…
Box dimension of trajectories of some discrete dynamical systems
Neven Elezović, Vesna Županović, Darko Žubrinić
We study the asymptotics, box dimension, and Minkowski content of trajectories of some discrete dynamical systems. We show that under very general conditions, trajectories correspo…