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Unformatted text preview: odel Example (continued)
Probability of moving through state i to i + 1 and being in
state i + 2 in t years from now
0 t µi e −µi s µi +1 e −µi +1 (r −s ) e −µi +2 (t −r ) drds s So jump from i to i + 1 at time s then jump from i + 1 to
i + 2 at time r then stay in i + 2 from time r to time t 44/60 Actuarial Statistics – Module 5: Parametric methods: Markov Model
General Markov Model Estimation of Intensities
Estimation for the able-illness-death model for age interval x
to x + 1
able a, ill i , dead d with transition intensities
able to ill σx
ill to able ρx
able to dead µx
ill to dead νx observe for the i th life 45/60 Vi waiting time in the able state, V = N Vi
Wi waiting time in the ill state, W = N Wi
Si number of transitions able to ill, S = N Si
Ri number of transitions ill to able, R = N Ri
Di number of transitions able to dead, D = N Di
Ui number of transitions ill to dead, U = N Ui
i =1 S: Sick H:Healthy D: Dead Actuarial Statistics – Module 5: Parametric methods: Markov Model
General Markov Model Maximum l...
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This document was uploaded on 04/03/2014.
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