# An estimator for ratios of Poisson distributed quantities

A common task for national statistical institutes is to estimate the size of a subpopulation, with certain specific characteristics, as a proportion of a larger population or subpopulation. This paper discusses the probability density function for the stochastic variable that describes this proportion.
A common task for national statistical institutes is to estimate the size of a subpopulation, with certain specific characteristics, as a proportion of a larger population or subpopulation, in particular in a time series setting where this proportion is reported on a regular basis. This paper discusses the probability density function for the stochastic variable that describes this proportion, where the numerator is treated as realisations of a Poisson process, and the denominator is the sum of a fixed value and realisations of a Poisson process that is independent from the numerator.