13_AS_6_lec_a

For each individual i we have observed 1 2 the

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Unformatted text preview: ) from x + ai to x + bi 12/30 Actuarial Statistics – Module 6: Parametric models: Binomial and Poisson models Binomial model The actuarial estimate Example A mortality investigation on 9 lives aged between 65 and 66 was conducted. For each individual i , we have observed 1 2 the indicator di whether death occurred prior to censoring or not (di = 1 if death occurred prior to censoring, di = 0 if death was not observed) 3 13/30 the exact time since age 65 that life i came under observation and is censored is ai and bi , respectively the exact time since age 65 when death is observed: ti Actuarial Statistics – Module 6: Parametric models: Binomial and Poisson models Binomial model The actuarial estimate Given the following results Life 1 2 3 4 5 6 7 8 9 ai 0.2 0 0 0.5 0 0 0 0.2 0.4 bi 0.8 0.6 1 1 1 0.8 1 0.6 1 ti 0.7 0.5 0.45 0.75 di 0 0 0 0 0 1 1 1 1 we have Ex = 0.6 + 0.6 + 1 + 0.5 + 1 + 1 + 1 + 0.8 + 0.6 = 7.1 4 q= = 0.563 7.1 14/30 Actuarial Statistics – Module 6: Parametric models: Binomial and Poisson models Binomial model Central exposed to risk 1 Binomial model Without censoring With censoring The actuarial estimate Central exposed to risk Discussion 2 Poisson model Introduction Maximum Likelihood Estimation Link to 2-state Markov models 3 Discussion: Binomial, Poisson and Markov multi-...
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