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arXiv · 2111.05336

The Jacobi Theta Distribution

Caleb Deen Bastian·Grzegorz Rempala·Herschel Rabitz
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Abstract

We form the Jacobi theta distribution through discrete integration of exponential random variables over an infinite inverse square law surface. It is continuous, supported on the positive reals, has a single positive parameter, is unimodal, positively skewed, and leptokurtic. Its cumulative distribution and density functions are expressed in terms of the Jacobi theta function. We describe asymptotic and log-normal approximations, inference, and a few applications of such distributions to modeling.

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Caleb Deen Bastian, Grzegorz Rempala, Herschel Rabitz. 2021-11-09. The Jacobi Theta Distribution. https://arxiv.org/abs/2111.05336

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