Meteor count rate time series collected during showers are a prime source of data for characterizing meteor streams. Doing so requires corrections for the sporadic meteor background, for the radiant positions in the sky, and for the specific properties of the observing equipment. This paper presents a suite of methods for analyzing meteor shower count rate time series using variants of the single- and double-exponential shower activity model. The approach relies on a least-squares fitting procedure. It is demonstrated that the basic version of the problem is often ill-posed. Constraining the fitting procedure by making assumptions about the sporadic background offers a partial remedy. To allow for a more robust solution, however, a generalization is developed that includes data from multiple observers. This makes the technique especially powerful when analyzing the data from forward scatter radio meteor networks. A Monte Carlo approach allows to establish confidence intervals on the results obtained. A selection of results illustrates the capabilities and limitations of these methods.