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Unformatted text preview: σ , ν , ρ) has an asymptotic multivariate Normal distribution
(µ, σ , ν , ρ) are asymptotically independent
Similar calculations as the simple 2 state model provides
E [V ] σ ∼ Normal σ, σ
E [V ] ν
E [W ] ρ ∼ Normal ρ, ρ
E [W ] µ ∼ Normal µ, ν ∼ Normal ν, 51/60 Actuarial Statistics – Module 5: Parametric methods: Markov Model
General Markov Model For a general Markov model, MLE µij of the transition rates
µij (j = i ):
µij ∼ Normal µij ,
E [Ti ]
where Ti is the total waiting time in state i . 52/60 Actuarial Statistics – Module 5: Parametric methods: Markov Model
General Markov Model Example A multiple state model has four states 1,2,3 and 4. For
states i = 2 and 3, a life can go directly either to i − 1 or to i + 1.
For state i = 1, a life can only go i + 1. For state i = 4, a life can
only go to i − 1. The force of transition from state i to state j is
equal to λ when i < j , and µ when i > j . A large number of lives
are in the system and they all beh...
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This document was uploaded on 04/03/2014.
- Three '14