  We consider a compositional data analysis approach to forecasting the age
distribution of death counts. Using the age-specific period life-table death
counts in Australia obtained from the Human Mortality Database, the
compositional data analysis approach produces more accurate one- to
20-step-ahead point and interval forecasts than Lee-Carter method,
Hyndman-Ullah method, and two na\"{i}ve random walk methods. The improved
forecast accuracy of period life-table death counts is of great interest to
demographers for estimating survival probabilities and life expectancy, and to
actuaries for determining temporary annuity prices for various ages and
maturities. Although we focus on temporary annuity prices, we consider
long-term contracts which make the annuity almost lifetime, in particular when
the age at entry is sufficiently high.
