The Difference-of-Log-Normals Distribution: Properties, Estimation, and Growth
Methodology
2023-02-14 v1 Statistics Theory
General Finance
Statistics Theory
Abstract
This paper describes the Difference-of-Log-Normals (DLN) distribution. A companion paper makes the case that the DLN is a fundamental distribution in nature, and shows how a simple application of the CLT gives rise to the DLN in many disparate phenomena. Here, I characterize its PDF, CDF, moments, and parameter estimators; generalize it to N-dimensions using spherical distribution theory; describe methods to deal with its signature ``double-exponential'' nature; and use it to generalize growth measurement to possibly-negative variates distributing DLN. I also conduct Monte-Carlo experiments to establish some properties of the estimators and measures described.
Keywords
Cite
@article{arxiv.2302.02486,
title = {The Difference-of-Log-Normals Distribution: Properties, Estimation, and Growth},
author = {Robert Parham},
journal= {arXiv preprint arXiv:2302.02486},
year = {2023}
}