This article proposes a probabilistic model for synthesizing room impulse responses (RIRs) for use in convolution artificial reverberators. The proposed method is based on the concept of echo density. Echo density is a measure of the number of echoes per second in an impulse response and is a demonstrated perceptual metric of artificial reverberation quality. As echo density is related to the statistical measure of kurtosis, this article demonstrates that the statistics of an RIR can be modeled using a probabilistic mixture model. A mixture model designed specifically for modeling RIRs is proposed. The proposed method is useful for statistically replicating RIRs of a measured environment, thereby synthesizing new independent observations of an acoustic space. A perceptual pilot study is carried out to evaluate the fidelity of the replication process in monophonic and stereo artificial reverberators.