The hybrid Gompertz distribution - derivation, characterization and estimation (a reaction network treatment)

Abstract

Using the tools of reaction network theory, we show how the well-known Gompertz probability distribution can be generalized to a new distribution - the hybrid Gompertz distribution. We characterize the hybrid Gompertz distribution using a combination of analytical and numerical methods, and compare it graphically to the standard Gompertz distribution. Selected probabilistic properties of the hybrid Gompertz distribution are presented and possible approaches to its estimation are investigated.

Acknowledgments. The work of Meglena Lazarova is supported by the Bulgarian National Science Fund under Project KP-06-M62/1 "Numerical deterministic, stochastic, machine and deep learning methods with applications in computational, quantitative, algorithmic finance, biomathematics, ecology and algebra" from 2022.