Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 207 / 4 / b / ii

Table of contents
- Solution ii

Solution

For

T =

age at death minus

60

, the observations are

2, 7, 1 4^{+}, 15, 1 9^{+}, 2 1^{+} .

There are three distinct event times and hence three independent discrete hazards

q_{2}, q_{7}, q_{15}

. Their risk-set sizes are

6, 5, 3

, so

L (q_{2}, q_{7}, q_{15}) = q_{2} (1 - q_{2})^{5} q_{7} (1 - q_{7})^{4} q_{15} (1 - q_{15})^{2} .

The maximum-likelihood estimates are

q_{2} = 1/6

,

q_{7} = 1/5

, and

q_{15} = 1/3

.

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