Extreme shock models: an alternative perspective

TL;DR

This paper introduces a Bayesian nonparametric approach to extreme shock models using reinforced urn processes, offering new insights into system failure prediction under random shocks.

Contribution

It presents an alternative perspective on extreme shock models through reinforced urn processes, enabling Bayesian predictive analysis of system failures.

Findings

Provides a Bayesian predictive distribution for system defaults.

Offers a new nonparametric framework for extreme shock modeling.

Enhances understanding of shock impact on system reliability.

Abstract

Extreme shock models have been introduced in Gut and H\"usler (1999) to study systems that at random times are subject to shock of random magnitude. These systems break down when some shock overcomes a given resistance level. In this paper we propose an alternative approach to extreme shock models using reinforced urn processes. As a consequence of this we are able to look at the same problem under a Bayesian nonparametric perspective, providing the predictive distribution of systems' defaults.