13_AS_9_lec_a

# Ds t 0 s px ds t qx t 0 s px ds the statistical

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Unformatted text preview: px µx +s ds t 0 s px ds = t qx t 0 s px ds The statistical estimate for mx ,t is no . of death , exposure which is called “occurrence-exposure rates”. Note that if µx +s is constant for 0 ≤ s < t and equal to µ, then m x ,t = 5/15 t 0 s px µds t 0 s px ds =µ Actuarial Statistics – Module 9: Standardization and new developments Crude Mortality rate 1 Introduction: Single Index Approach 2 Crude Mortality rate 3 Directly standardized mortality rate 4 Indirectly Standardized Mortality Rate 5 The standardized mortality ratio 6 More advanced mortality models 6/15 Actuarial Statistics – Module 9: Standardization and new developments Crude Mortality rate Crude Mortality rate The crude mortality rate (note: single index) is deﬁned as Total Actual Deaths = Total Exposed-to-Risk x c Ex ,t mx ,t x c E x ,t , which is a weighted average of mx ,t (age speciﬁc death rates). Note it only requires total deaths and total waiting time (age-speciﬁc quantities not relevant). 6/15 Actuarial Statistics – Module 9: Standardization and new developments Crude Mortality rate Example Consider the following two towns. Town A Town B Age Population Deaths Population 20 70000 210 10000 40 20000 90 20000 60 10000 100 70000 We have CMRA = 7/15 400 = 0.4% 100, 000 and CMRB = Deaths 15 60 525 600 = 0.6% > CMRA 100, 000 Actuarial Statistics – Module 9: Standardization and new developments Crude Mortality rate Note that the age speciﬁc rates are Age 20 40 60 Town A Population 70000 20000 10000 Deat...
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## This document was uploaded on 04/03/2014.

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