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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 “occurrenceexposure 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 ExposedtoRisk 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
(agespeciﬁc 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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