The Jacobi Theta Distribution
Probability
2021-11-11 v1 Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.2111.05336,
title = {The Jacobi Theta Distribution},
author = {Caleb Deen Bastian and Grzegorz Rempala and Herschel Rabitz},
journal= {arXiv preprint arXiv:2111.05336},
year = {2021}
}
Comments
16 pages, 8 figures