In this work, we aim to represent tactile textures in such a way that a given texture may be "painted" onto a selected spatial region of a tactile display. We recorded a series of fingertip swipes across eleven textures and stored the data as spatial friction maps - friction as a function of position. We analyzed these maps with a space-frequency transform, and observed stochasticity in our physical measurements. We modeled the randomness in spectral magnitude across space with three distributions: Rayleigh, Rice, and Weibull. We analyzed the quality of parameterizations using goodness of model fit as well as consistency across multiple swipes of the same texture. We found that a two-parameter Weibull model best represented the measured data, and propose to use this model in the Tactile Paintbrush for applying virtual textures to spatial regions.