Mortality Tables Flashcards
Notation for life tables: lx
number of lives in the table at time x
Notation for life tables: dx
expected number of deaths among the lx
Notation for life tables: qx
probability of dying within one year at x
Notation for life tables: px
probability of surviving one year at x
Notation for life tables: ex
expected number of complete years lived for life of age x
Notation for life tables: ω
value of x at which values of lx become zero or negligible
Notation for life tables: µx
force of mortality at age x
Notation for life tables: mx
rate of mortality at age x
how do you find dx
lx - l(x+1)
how do you find qx
(lx - l(x+1)) / lx
how do you find px
1 - qx
how do you find ex
sum(x+1 to infinity) lx / lx
how do you find µx
- 1 / lx * d/dx (lx)
assuming constant hazard between x and x+1, what is µx
- log(px)
what is the probability of dying in time x to x+1
exp(-H(x)) * exp(-H(x+1))
how do you find mx
dx / (lx - dx/2)
what is nQx
probability a life aged x will die in n years
note nQx = 1 - nPx
formula for nPx
l(x+n) / lx
what is m|nQx
probability a life aged x will die between ages x+m and x+m+n
formula for m|nQx
l(x+m+n) - l(x+n) / lx
How is lx related to the integrated hazard function?
lx = l0 * exp( - H(x) )
how do you get nPx from force of mortality
exp( - ∫(x to x+n) µt dt )
Interpolate using linear interpolation
l(x+t) = lx + t( l(x+1) - lx )
Interpolate using exponential interpolation
l(x+t) = lx * px^t
