Les lois de probabilite pour les fonctions statistiques (cas de collectifs a plusieurs dimensions)

TL;DR

This paper generalizes the convergence of statistical functions to Gaussian distributions from one-dimensional to multi-dimensional collectives, extending classical probability laws.

Contribution

It extends M. de Mises' 1936 results on the Gaussian convergence of statistical functions to cases involving multi-dimensional collectives.

Findings

Generalization of Gaussian convergence for multi-dimensional collectives

Extension of classical probability laws to higher dimensions

Theoretical framework for multi-dimensional statistical functions

Abstract

In a memoir published in 1936 in the Annales de Institut Poincare, M. de Mises demonstrates that under certain conditions, the distribution (law of probability) of the so-called statistical functions tends towards the Gaussian, the collectives being assumed to have one dimension. In the present presentation, I propose to generalize this property in the case where the collectives are with several dimensions.