The generalized age distribution for any population in continuous time obtained by Bennett and Horiuchi (1981) and Preston and Coale (1982) is derived in the discrete time formulation in the first part of this paper. Other expressions that follow from the age distribution in Preston-Coale are also presented in discrete time and age. Then the Preston-Coale procedure of using these expressions to estimate mortality when demographic data are defective is critically examined. It is noted that the series of age-specific growth rates, the essential feature of the new expressions, reflects defective census age distributions exactly so that a demographic measure estimated by the Preston-Coale procedure is still affected by the defective data.

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