✦ LIBER ✦

Discrete Normal distribution and its relationship with Jacobi Theta functions

✍ Scribed by Paweł J. Szabłowski

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 120 KB
Volume: 52
Category: Article
ISSN: 0167-7152
DOI: 10.1016/s0167-7152(00)00223-6

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✦ Synopsis

We introduce new, natural parameters in a formula deÿning 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 su ciently large variances and all expectations, discrete Normal distributions and their ÿrst two moments are given by very simple formulae. We indicate the relation between our results and Jacobi Theta functions and Jacobi summation formulae.