On harmonic oscillator hazard functions

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.