This means that if there is only one transition

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Unformatted text preview: ctuarial 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-state models 25/30 Actuarial Statistics – Module 6: Parametric models: Binomial and Poisson models Poisson model Link to 2-state Markov models In a Markov model, changes of state occur according to a Poisson process (otherwise not Markov). This means that if there is only one transition possible (from life to death), the number of deaths behaves like a Poisson random variable Under the two-state Markov model E [˜] = µ and var [˜] = E [µ ] µ µ V Under the Poisson models: µ E [˜] = µ and var [˜] = E c µ µ x c µ and E [V ] are unknown and must be estimated by µ and Ex , ˆ respectively. So the numerical estimates of the parameter and the moments of the estimator are same for both models. Difference is that in the Markov model you can specify that a transition from death to life is impossible, whereas with a straight Poisson rv you assume that individuals can die several times 25/30 Actuarial Statistics – Module 6: Parametric models: Binomial and Poisson models Discussion: Binomial, Poisson and Markov multi-state models Underlying processes binomial model allows for death or survival but it represents...
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This document was uploaded on 04/03/2014.

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