On harmonic oscillator hazard functions

TL;DR

This paper introduces a new parametric hazard model based on the damped harmonic oscillator, providing closed-form functions that can model diverse hazard shapes and facilitate inference in survival analysis.

Contribution

The paper presents a novel hazard model derived from the damped harmonic oscillator with closed-form hazard functions, enabling flexible modeling and inference.

Findings

Model captures various hazard shapes including oscillatory patterns.

Closed-form hazard and cumulative hazard functions facilitate inference.

Demonstrated effectiveness on real survival data.

Abstract

We propose a parametric hazard model obtained by enforcing positivity in the damped harmonic oscillator. The resulting model has closed-form hazard and cumulative hazard functions, facilitating likelihood and Bayesian inference on the parameters. We show that this model can capture a range of hazard shapes, such as increasing, decreasing, unimodal, bathtub, and oscillatory patterns, and characterize the tails of the corresponding survival function. We illustrate the use of this model in survival analysis using real data.