Calcium imaging has emerged as an important tool for measuring the activities of large neural populations. Much effort has been devoted to developing pre-processing tools, addressing the important issues of e.g., motion correction, extraction of regions of interest, and spike inference. However, computational modeling of deconvolved calcium signals (i.e., the estimated activity extracted by a pre-processing pipeline) is just as critical for interpreting calcium measurements. Surprisingly, these issues have received less attention. To fill this gap, we examine the statistical properties of the deconvolved signals, and propose several density models for these random signals. These models include a Spike+Gamma model, which characterizes the calcium responses as a mixture of a gamma distribution and a point mass (“spike") which serves to model zero responses. We apply the resulting models to neural encoding and decoding problems. We find that the Spike+Gamma model outperforms simpler models (e.g., Poisson or Bernoulli models) for both simulated and real neural data. This Spike+Gamma model may pave the way for improved quantitative modeling of large scale calcium responses.