Elements of the Kopula (eventological copula) theory

TL;DR

This paper introduces the concept of Kopula in eventology, establishing a theorem that characterizes sets of events and drawing parallels to classical copula theory, with specific examples for small event sets.

Contribution

It presents the novel concept of Kopula in eventology and proves a key theorem linking event sets to Kopulas, extending classical copula ideas.

Findings

Kopula concept introduced in eventology.

Proved theorem characterizing event sets via Kopula.

Provided explicit forms of Kopulas for small event sets.

Abstract

New in the probability theory and eventology theory, the concept of Kopula (eventological copula) is introduced. The theorem on the characterization of the sets of events by Kopula is proved, which serves as the eventological pre-image of the well-known Sclar's theorem on copulas (1959). The Kopulas of doublets and triplets of events are given, as well as of some N-sets of events.