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Discrete normal distribution and its relationship with Jacobi theta functions. (English) Zbl 1081.60012
Summary: We introduce new, natural parameters in a formula defining a family of discrete normal distributions. One of the parameters is closely related to the expectation and the other to the variance of that family. We show that under such a parametrization, uniformly for all sufficiently large variances and all expectations, discrete normal distributions and their first two moments are given by very simple formulae. We indicate the relation between our results and Jacobi Theta functions and Jacobi summation formulae.

MSC:
60E05 Probability distributions: general theory
62E10 Characterization and structure theory of statistical distributions
11F27 Theta series; Weil representation; theta correspondences
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