Sounds like "running water" and "buzzing bees" are classes of sounds which are a collective result of many similar acoustic events and are known as "sound textures". A recent psychoacoustic study using sound textures has reported that natural sounding textures can be synthesized from white noise by imposing statistical features such as marginals and correlations computed from the outputs of cochlear models responding to the textures. The outputs being the envelopes of bandpass filter responses, the 'cochlear envelope'. This suggests that the perceptual qualities of many natural sounds derive directly from such statistical features, and raises the question of how these statistical features are distributed in the acoustic environment. To address this question, we collected a corpus of 200 sound textures from public online sources and analyzed the distributions of the textures' marginal statistics (mean, variance, skew, and kurtosis), cross-frequency correlations and modulation power statistics. A principal component analysis of these parameters revealed a great deal of redundancy in the texture parameters. For example, just two marginal principal components, which can be thought of as measuring the sparseness or burstiness of a texture, capture as much as 64% of the variance of the 128 dimensional marginal parameter space, while the first two principal components of cochlear correlations capture as much as 88% of the variance in the 496 correlation parameters. Knowledge of the statistical distributions documented here may help guide the choice of acoustic stimuli with high ecological validity in future research.