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Unformatted text preview: ctuarial estimate
Central exposed to risk
2 Poisson model
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
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 ]
Under the Poisson models:
E [˜] = µ and var [˜] = E c
µ and E [V ] are unknown and must be estimated by µ and Ex ,
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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