Mortality Tables

Question 1

Notation for life tables: lx

Answer 1

number of lives in the table at time x

Question 2

Notation for life tables: dx

Answer 2

expected number of deaths among the lx

Question 3

Notation for life tables: qx

Answer 3

probability of dying within one year at x

Question 4

Notation for life tables: px

Answer 4

probability of surviving one year at x

Question 5

Notation for life tables: ex

Answer 5

expected number of complete years lived for life of age x

Question 6

Notation for life tables: ω

Answer 6

value of x at which values of lx become zero or negligible

Question 7

Notation for life tables: µx

Answer 7

force of mortality at age x

Question 8

Notation for life tables: mx

Answer 8

rate of mortality at age x

Question 9

how do you find dx

Answer 9

lx - l(x+1)

Question 10

how do you find qx

Answer 10

(lx - l(x+1)) / lx

Question 11

how do you find px

Answer 11

1 - qx

Question 12

how do you find ex

Answer 12

sum(x+1 to infinity) lx / lx

Question 13

how do you find µx

Answer 13

• 1 / lx * d/dx (lx)

Question 14

assuming constant hazard between x and x+1, what is µx

Answer 14

• log(px)

Question 15

what is the probability of dying in time x to x+1

Answer 15

exp(-H(x)) * exp(-H(x+1))

Question 16

how do you find mx

Answer 16

dx / (lx - dx/2)

Question 17

what is nQx

Answer 17

probability a life aged x will die in n years

note nQx = 1 - nPx

Question 18

formula for nPx

Answer 18

l(x+n) / lx

Question 19

what is m|nQx

Answer 19

probability a life aged x will die between ages x+m and x+m+n

Question 20

formula for m|nQx

Answer 20

l(x+m+n) - l(x+n) / lx

Question 21

How is lx related to the integrated hazard function?

Answer 21

lx = l0 * exp( - H(x) )

Question 22

how do you get nPx from force of mortality

Answer 22

exp( - ∫(x to x+n) µt dt )

Question 23

Interpolate using linear interpolation

Answer 23

l(x+t) = lx + t( l(x+1) - lx )

Question 24

Interpolate using exponential interpolation

Answer 24

l(x+t) = lx * px^t