Existing methods for estimating population parameters in settings of data deficiency do not provide techniques for analysis of commonly available longitudinal data. In settings where complete population data is unavailable, longitudinal data recorded for only a subset of the total population are often available (e.g., event registers, genealogies). In this article we present and evaluate models which derive population parameters for the population subgroup underlying such longitudinal data. Using the distribution of individual times until first recorded event within a measurement interval, population parameters are estimated which provide basic denominator data for analyzing event occurrence. The models which we derive are especially suited to records which may include migration and population growth trends. The use of the models is demonstrated and evaluated through an application to genealogical records for a nineteenth-century population. Possible extensions of these models and their major limitations are also discussed.