# Estimating age distribution from first names

Is it possible to estimate an age distribution of a specific population (e.g. actors, customers, etc.) from a list of their first names? Given that data of the number of individuals grouped by birth year, first name and sex of the total population (e.g. Swedish population) are available for use.

The age distribution of the specific population might not be the same as the total population.

Although I can’t figure out how to solve this, my idea is that it should be possible to have an estimation since all first names have their unique distributions. For example, let's assume John and Marcus have the same average age in the total population, but that their distributions differs, and if there happens to be more individuals named John in our sample, it might imply that our specific distribution is closer to John’s than to Marcus’.

Is this even possible - and if so - what approach would you suggest? Thanks!

This seems trivial. If you have age and first name for the total population, you have age distribution for each first name $p(Age=A|Name=N)$ . Then given the list of names for some subpopulation S, you have
$p_S(Age=A) = \sum_N p_S(Name=N) p(Age=A|Name=N)$
where $p_S(Age=A)$ is the age distribution of subpopulation $S$, and $p_S(Name=N)$ is the name distribution of this subpopulation.