IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Maximum likelihood estimators for transition intensities
In a two-decrement model (alive to dead by cause 1 or cause 2), 500 life-years of exposure produced 15 deaths from cause 1 and 10 from cause 2. Assuming constant intensities, what is the maximum likelihood estimate of the probability that a life aged exactly x survives one year in the alive state?
The survival probability is exp(-0.05), because the estimated constant intensities are 0.03 and 0.02 from 15 and 10 deaths over 500 life-years, and survival over one year depends on their sum.
- Aexp(-0.03)
- Bexp(-0.05)Correct
- Cexp(-0.02)
- D1 - 0.05
- exp(-0.5)
Explanation
mu1 = 15/500 = 0.03 and mu2 = 10/500 = 0.02. Total intensity 0.05, so the one-year survival probability is exp(-0.05). Using only cause 1 gives exp(-0.03), which ignores the other decrement; 1-0.05 is a linear approximation, not the model value.
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