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

In a study of lifetimes of policyholders in a pension scheme, an individual is observed from entry until the study ends, at which point the person is still alive. Assuming the censoring is non-informative, what is this individual's contribution to the likelihood?

A right-censored individual contributes the survival function at the censoring time, S(c), divided by S at entry if there is left truncation. This is because we only know the life survived beyond c, not when death occurs, so the density is not used.

  1. AThe density function f(x) at the censoring time
  2. BThe survival function S(c) at the censoring time, conditional on survival to entry if there is left truncationCorrect
  3. CThe hazard function at the censoring time
  4. DThe distribution function F(c) at the censoring time
  5. The probability that death occurs exactly at the censoring time

Explanation

A right-censored life is known only to have survived beyond the censoring time c, so its contribution is P(T>c), i.e. S(c). If the life entered late, the contribution is S(c)/S(entry). The density applies only to observed deaths.

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