# Kinetic modeling of alcohol consumption

## TL;DR

This paper models alcohol consumption distributions using kinetic theory, explaining their shape through microscopic agent interactions and deriving a generalized Gamma distribution as the equilibrium.

## Contribution

It introduces a kinetic model based on prospect theory to explain the emergence of Gamma and Weibull distributions in alcohol consumption data.

## Key findings

- Alcohol consumption distributions can be modeled by a generalized Gamma distribution.
- Microscopic agent interactions determine the macroscopic distribution shape.
- The model clarifies the meaning of parameters in the equilibrium distribution.

## Abstract

In most countries, alcohol consumption distributions have been shown to possess universal features. Their unimodal right-skewed shape is usually modeled in terms of the Lognormal distribution, which is easy to fit, test, and modify. However, empirical distributions often deviate considerably from the Lognormal model, and both Gamma and Weibull distributions appear to better describe the survey data. In this paper we explain the appearance of these distributions by means of classical methods of kinetic theory of multi-agent systems. The microscopic variation of alcohol consumption of agents around a universal \emph{social} accepted value of consumption, is built up introducing as main criterion for consumption a suitable value function in the spirit of the prospect theory of Kahneman and Twersky. The mathematical properties of the value function then determine the unique macroscopic equilibrium which results to be a generalized Gamma distribution. The modeling of the microscopic kinetic interaction allows to clarify the meaning of the various parameters characterizing the generalized Gamma equilibrium.