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
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
