Multivariate compounds with equal number of summands

TL;DR

This paper studies multivariate discrete sums with equal summands, deriving properties and formulas relevant to insurance, queuing, and branching processes, providing new insights into their distributions and characteristics.

Contribution

It introduces general properties and formulas for multivariate sums with equal summands, expanding understanding across multiple application domains.

Findings

Derived properties and formulas for these distributions

Analyzed particular cases of multivariate sums

Connected distributions to applications in insurance, queuing, and branching processes

Abstract

The paper considers multivariate discrete random sums with equal number of summands. Such distributions describe the total claim amount received by a company in a fixed time point. In Queuing theory they characterize cumulative waiting times of customers up to time t. In Theory of branching processes they model the number of heirs at a fixed point in time. Here some general properties and formulae for numerical characteristics of these distributions are derived and some particular cases are considered.