Glossary Entry

Hazard Function

The instantaneous or per-period risk of an event occurring at time t, conditional on having survived up to t. High early hazard means early failures; spikes mark risky moments like contract expiries.

Statistics Models

Also called: hazard rate, churn hazard, hazard functions

Seed source: lifelines, Introduction to survival analysis

The hazard reframes lifetime risk as a sequence of conditional questions: given survival so far, what is the chance of the event happening right now? For monthly customer data it is simply “what fraction of customers who reached month t churn during month t?”, which is why hazards tend to match business intuition better than raw lifetime distributions.

Mechanisms live in the hazard. Onboarding friction appears as elevated hazard in the first months, contract ends as sharp spikes, and loyalty effects as a slow decline. The survival function is recovered by multiplying up the per-period survival probabilities, one minus the hazard at each step, which is exactly the structure the Kaplan-Meier estimator exploits.