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STAT3801_2011Unit3[1]

# STAT3801_2011Unit3[1] - THE UNIVERSITY OF HONG KONG...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT3801 ADVANCED LIFE CONTINGENCIES Unit 3 2010-11 2 nd semester 3.1 Single state model - ALIV E DEAD die Examples Basic survival models Multiple-decrement survival models Multiple-life models Basic survival models Intact Failed

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S&AS: STAT3801 ADVANCED LIFE CONTINGENCIES 2 Multiple-decrement survival models Intact Failed for Cause # 1 Failed for Cause # 2 · · · Failed for Cause # m Multiple-life models 0. Both ( x ) and ( y ) are intact 1. ( x ) is intact but ( y ) has failed 2. ( y ) is intact but ( x ) has failed 3. Both ( x ) and ( y ) have failed
S&AS: STAT3801 ADVANCED LIFE CONTINGENCIES 3 3.2 Multiple state model ? - ? DEAD HEALTHY SICK 0 1 2 Multi-state transition models Each individual subject is in 1 of several states Individuals can make transitions Rates are determined by forces of transition

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S&AS: STAT3801 ADVANCED LIFE CONTINGENCIES 4 Disability model 0 = Active 1 = Temporarily Disabled 2 = Permanently Disabled 3 = Inactive Driver ratings 1 = Preferred 2 = Standard 3 = Substandard 4 = Gone Continuing Care Retirement Communities(CCRC’s) 0 = Independent Living 1 = Temporarily in Health Center 2 = Permanently in Health Center 3 = Gone
S&AS: STAT3801 ADVANCED LIFE CONTINGENCIES 5 Pension model - ? ? - ? ? @ @ @ @ @ @ @ @ @ R ? ? death ( d ) employed or active ( a ) ill or disabled ( i ) voluntary termination ( w ) retirement ( r ) Multi-state transition models An absorbing state is one which, - once entered cannot subsequently left A transient state is not necessarily permanent

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S&AS: STAT3801 ADVANCED LIFE CONTINGENCIES 6 Disability model ? - ? ? ? ? Active Inactive Permanently Disabled Temporarily Disabled 0 1 2 3 This model has four states 0 = Active 1 = Temporarily Disabled 2 = Permanently Disabled 3 = Inactive
S&AS: STAT3801 ADVANCED LIFE CONTINGENCIES 7 There are five transition probabilities = 0 from # 2 to # 0, from # 2 to # 1 and from # 3 to # j, j = 0 , 1 , 2 Transition probabilities depend on age of individual Some may also depend on duration State number M n = State number at time n

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S&AS: STAT3801 ADVANCED LIFE CONTINGENCIES 8 3.3 Transition probabilities-Markov chains
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STAT3801_2011Unit3[1] - THE UNIVERSITY OF HONG KONG...

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