For forensic purposes, short tandem repeat allele signals are used as DNA fingerprints. The interpretation of signals measured from samples has traditionally been conducted by applying thresholding. More quantitative approaches have recently been developed, but not for the purposes of identifying an appropriate signal model. By analyzing data from 643 single person samples, we develop such a signal model. Three standard classes of two-parameter distributions, one symmetric (normal) and two right-skewed (gamma and log-normal), were investigated for their ability to adequately describe the data. Our analysis suggests that additive noise is well modeled via the log-normal distribution class and that variability in peak heights is well described by the gamma distribution class. This is a crucial step towards the development of principled techniques for mixed sample signal deconvolution.