Single-point measurements of fluctuations in the scrape-off layer of magnetized plasmas are generally found to be dominated by large-amplitude bursts which are associated with radial motion of bloblike structures. A stochastic model for these fluctuations is presented, with the plasma density given by a random sequence of bursts with a fixed wave form. When the burst events occur in accordance to a Poisson process, this model predicts a parabolic relation between the skewness and kurtosis moments of the plasma fluctuations. In the case of an exponential wave form and exponentially distributed burst amplitudes, the probability density function for the fluctuation amplitudes is shown to be a Gamma distribution with the scale parameter given by the average burst amplitude, and the shape parameter given by the ratio of the burst duration and waiting times.