When a human is infected with influenza, the amount of virus produced in the upper respiratory tract increases exponentially for 1-2 days and then declines exponentially. This simple dynamic can be reproduced by a wide variety of mathematical models of viral infection which, when utilized to fit the data, will predict different values for the underlying infection kinetics parameters. We analyze in vitro influenza infection experimental data from the literature, specifically that of single-cycle viral yield experiments, to narrow the range of applicable models. In particular, we demonstrate the viability of using normal or lognormal distributions to characterize the time a cell will spend in a given infection state (e.g., the time spent by a newly infected cell in the latent state before it begins to produce virus), and the shortcomings of using delta distributions or the exponential distributions implicit to ordinary differential equation models.