We will present new results concerning the accuracy with which the basis coefficients that define an inhomogeneous Poisson process can be recovered using maximum-likelihood estimation. These results generalize existing guarantees that only hold when observing a Poisson counting process, i.e., a discretized version of the more-general Poisson arrival process. In the process, we remove several restrictive assumptions. We conclude with a brief discussion of applications of these results to more complex models such as Hawkes processes.