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BUS3018F: Chapter 6 Summary

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A complete summary of the survival models (chapter 6) section for BUS3018F. Contains all important formula, relationships and tips. Does not contain proofs of each relationship. High quality pdf.

Last document update: 2 year ago

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  • February 17, 2022
  • February 17, 2022
  • 10
  • 2021/2022
  • Summary

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By: elainesamuel • 1 year ago

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Chapter 6
Summary
T -
future lifetime of newborn person


Tx future lifetime of X
person aged
-




w -



limiting age

Rate of
Mortality
Fx (t) = Pr Tx ← t
=
t 9✗

f-✗ (t) =
t Px llxtt
.




Survival Probabilities

S ✗ (t ) = Pr Tx > t
=
I -

Fx (t ) >
t Px = I -



tax
=
t P*

Consistency condition : set Px =
s Px .
t Poets

-
Sot µx+s .
ds
t Px =
e


> used often .

, >
transitioning
Instantaneous rate of
from alive to dead state
Force of
Mortality
him
'

n Pr Tx < t -1h Tx > t
µ×
= , o




complete Expectation of life

W - X



éx = E ( Tx ) =
So + Px .
dt


Curate Lifetimes

Kx = Tx
value of Tx
largest integer
=




> discrete over ( o to w -
x




PMF of Kx : Pr Kx = k =
KPX .
9×+14
=
K Cfx


curtate Expectation of life
W - X



ex = I kpx
K=I

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