13_AS_6_lec_a

# This means that if there is only one transition

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This document was uploaded on 04/03/2014.

Ask a homework question - tutors are online