On partially Schur-constant models and their associated copulas

Claude Lefèvre

doi:10.1515/demo-2021-0111

Abstract

Abstract Schur-constant vectors are used to model duration phenomena in various areas of economics and statistics. They form a particular class of exchangeable vectors and, as such, rely on a strong property of symmetry. To broaden the field of applications, partially Schur-constant vectors are introduced which correspond to partially exchangeable vectors. First, their copulas of survival, said to be partially Archimedean, are explicitly obtained and analyzed. Next, much attention is devoted to the construction of different partially Schur-constant models with two groups of exchangeable variables. Finally, partial Schur-constancy is briefly extended to the modeling of nested and multi-level dependencies.

Highlights

Schur-constant vectors play a central role in modeling lifetime data in actuarial science, reliability and survival analysis
Schur-constant vectors are used to model duration phenomena in various areas of economics and statistics. They form a particular class of exchangeable vectors and, as such, rely on a strong property of symmetry
We introduce a more general model, called partially Schur-constant, which is based on the property of partial exchangeability of a random vector ([16])

Summary

Introduction

Schur-constant vectors play a central role in modeling lifetime data in actuarial science, reliability and survival analysis. The following four sections concern the construction of di erent partially Schur-constant models with two groups of exchangeable variables. Xm) on IRn+ is partially Schur-constant if its joint survival function can be written in the form A survival function S : IRm+ → [ , ] may generate a partially Schur-constant vector (2.2) if and only if the function S is n =

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Conclusion