
General formulas for the central and noncentral moments of the multinomial distribution
We present the first general formulas for the central and noncentral mo...
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The crosssectional distribution of portfolio returns and applications
This paper aims to develop new mathematical and computational tools for ...
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New Developments on the NonCentral ChiSquared and Beta Distributions
New formulas for the moments about zero of the Noncentral ChiSquared a...
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Moments of the Distribution of Pearsons Correlation over Permutations of Data
Presented is an inductive formula for computing the exact moments of the...
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A Theory of Trotter Error
The LieTrotter formula, together with its higherorder generalizations,...
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The pAiry distribution
In this manuscript we consider the set of Dyck paths equipped with the u...
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Tail Bound Analysis for Probabilistic Programs via Central Moments
For probabilistic programs, it is usually not possible to automatically ...
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Handy Formulas for Binomial Moments
Despite the relevance of the binomial distribution for probability theory and applied statistical inference, its higherorder moments are poorly understood. The existing formulas are either not general enough, or not structured or simplified enough for intended applications. This paper introduces novel formulas for binomial moments, in terms of variance rather than success probability. The obtained formulas are arguably better structured and simpler compared to prior works. In addition, the paper presents algorithms to derive these formulas along with working implementation in the Python symbolic algebra package. The novel approach is a combinatorial argument coupled with clever algebraic simplifications which rely on symmetrization theory. As an interesting byproduct we establish asymptotically sharp estimates for central binomial moments, improving upon partial results from prior works.
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