Random Reward Phase-Type Distributions with Applications in Latent Severity Modeling

This paper proposes an extension to discrete Phase-Type distributions (DPH) by introducing random rewards. These allow for modeling a system in which a visit to a certain state does not emit a deterministic reward. Instead, the rewards follow either a Bernoulli or a geometric distribution. Utilizing this increased flexibility, we further sketch a possible use case for these random rewards by introducing the Inertia-Escalation model (IEM), a process with latent severity levels characterized through two parameters: Inertia {\nu} and escalation {\eta}. We also discuss parameter inference for such models. To validate and explore random rewards and the IEM, we conducted extensive simulations and applied the model to two datasets: historical warfare and the Telco customer churn dataset.