This post is the first in a series that will try to characterize lithic debitage assemblages formed from more than one reduction strategy. The primary goals are to estimate the proportions of the various reduction strategies represented within these mixed assemblages and to quantify the uncertainty of these estimates. I plan to use mixture models and the method of maximum likelihood to identify the distinct components of such assemblages.

Brown (2001) suggests that the distribution of debitage size follows a power law. Power law distributions have the following probability density function:

,

where *C* is a constant that normalizes the distribution, so the density integrates to one. The value of *C* thus depends entirely on the exponent .

Based on analysis of experimentally-produced assemblages, Brown further suggests that the exponent, , of these power law distributions varies among different reduction strategies. Thus, different reduction strategies produce distinctive debitage size distributions. This result could be very powerful, allowing reduction strategies from a wide variety of contexts to be characterized and distinguished. The technique used by Brown to estimate the value of the exponent, however, has some technical flaws.

Brown (2001) fits a linear regression to the relationship between the log of flake size grade and the log of the cumulative count of flakes in each size grade. In its favor, this approach seemingly reduces the effects of small sample sizes and can be easily replicated. The regression approach, on the other hand, also produces biased estimates of the exponent and does not allow the fit of the power law model to be compared to other probability density functions.

Maximum likelihood estimates, using data on the size of each piece of debitage, produce more reliable estimates of the exponent of a power law. Maximum likelihood estimates can also be readily compared among different distributions fit to the data, to evaluate whether a power law is the best model to describe debitage size distributions. The next post will illustrate the use of the linear regression approach and the maximum likelihood approach on simulated data drawn from a power law distribution.

**Reference cited**

Brown, Clifford T.

2001 The Fractal Dimensions of Lithic Reduction. *Journal of Archaeological Science* 28: 619-631.

© Scott Pletka and *Mathematical Tools, Archaeological Problems*, 2013