Paper - Statistics Singapore

Number of Survivors at Age x20. The number of persons living at age 0, l 0, is set at 100,000. For agesgreater than 0, the number of persons expected to be living at each age x is derivedusing the proportions dying in each age interval based on the formulal l − ( l q ) 1.x=x− 1 x−1×x−Number of Deaths between ages x and x+121. The number of persons expected to die between age x and x+1 is obtainedby applying the probability of dying at age x to the number of survivors at thebeginning of that age, that is, d = l × q .Number of Person-years Lived between ages x and x+1xxx22. L xis the number of person-years lived within the age interval x to x+1 bysurvivors at age x. For x ≥ 1, mortality is assumed to be evenly distributed withinthe age interval, and therefore L = xl + 0. x+ 15dxfor x ≥ 1.23. At age x = 0, deaths tend to be concentrated in the first few months of life.The formula for L0is therefore modified using the separation factor f0andcomputed as L = l + f .0 1 0d024. For the open-ended age group 100 years and over, L ∞ 100is calculated bysurviving the life table cohort from age 100 until the age at which L xis essentiallyzero. The corresponding values for ages 100 years and over are then summed togive .∞ L 100Total number of Person-Years Lived after Age x25. The total number of person-years expected to be lived by survivors at age x100∑ +=is obtained by using the formula T xL x.Life Expectancyx26. Life expectancy is the average number of years which a person living at agex is expected to live. It is derived by dividing the number of person-years expectedTxto be lived at age x by the number of survivors at age x, that is, ex= .lx5