From a Hierarchy of Stochastic Differential Equations to a Hierarchy of Generalized Beta Distributions
Updated
Updated · arxiv.org · Oct 7
From a Hierarchy of Stochastic Differential Equations to a Hierarchy of Generalized Beta Distributions
1 articles · Updated · arxiv.org · Oct 7
Summary
Researchers have developed a new hierarchy of generalized Beta distributions derived from a mean-reverting stochastic differential equation with three stochastic components.
This framework unifies finite-support, heavy-tailed, and exponential-type distributions, and introduces two distinct generalizations based on the order of nonlinear transformations.
The approach provides a stochastic basis for widely used statistical distributions, clarifying their interrelations and offering new perspectives for modeling in economics and physics.