V2 3 n2 2 and v3 3 n3 2 v3 3 actuarial statistics

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Unformatted text preview: ny further assumptions you make. Find the maximum likelihood estimates for the parameters σ1 , σ2 , and σ3 and expressions for their standard errors. 58/60 Actuarial Statistics – Module 5: Parametric methods: Markov Model General Markov Model Exercise (continued) Solution (i) Likelihood function − 1 ·v − 1 ·v − 1 ·v 1 1 1 l = ( σ1 )n1 · ( σ2 )n2 · ( σ3 )n3 · e σ1 1 e σ2 2 e σ3 3 where the total waiting time is T −1 vi = 0 Pi (t )dt ≈ T=0 Pi (k )+Pi (k +1) = k 2 −1 1 Pi (0) + T=1 Pi (k ) + 1 Pi (T ) for i = 1, 2, 3, k 2 2 assuming Pi (...
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This document was uploaded on 04/03/2014.

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