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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Estimation procedures for lifetime distributions

In a study of policyholder lifetimes, the Kaplan-Meier estimator of the survival function is computed. Which statement about the estimator is correct?

The Kaplan-Meier estimator is a step function that falls only at observed death times. Censoring changes the number at risk but causes no drop itself. It is non-parametric and handles right-censored data, so the other statements are false.

  1. AIt is a step function that changes value only at observed death timesCorrect
  2. BIt changes value at every observed time, including censoring times
  3. CIt always reaches zero at the largest observation
  4. DIt assumes lifetimes follow an exponential distribution
  5. It cannot be used when any observations are right-censored

Explanation

The Kaplan-Meier estimator is a non-parametric product-limit estimate. It drops only at times when deaths occur; censoring times alter the risk set but not the estimate directly. It does not reach zero if the largest observation is censored, and it is designed for censored data.

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