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census data often available with number in each state
recorded at ﬁxed dates (e.g. 31 December)
estimate waiting times by making some simplifying
assumptions, eg assuming transitions occur on average half
way through the interval 57/60 Actuarial Statistics – Module 5: Parametric methods: Markov Model
General Markov Model Exercise A multiple state model has three states. From state 1,
1
lives can only jump to state 2 with transition force σ1 . From state
1
2, they can only jump to state 3 with transition force σ2 and from
1
state 3, they can only jump to state 1 with transition force σ3 . All
transition forces are constant. Lives can also enter or exit out of
the system at any time. Entry and exit times are deterministic.
The system is inspected regularly and Pi (t ) denotes the observed
number of lives in state i at time t (t = 0, 1,2, · · · , T). ni denotes
the observed number of transitions out of state i over the time
period [0, T] (not including the exits).
(i) Write down the likelihood function stating a...
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