I would suggest that, by using proved statistical theory regarding atypical distribution of data it may be possible to determine a rough understanding of the minimum time frame of human occupation of the Americas.

Lithic artifact
distribution in the Americas is probably related to population
density.

To do this, we must
ignore the arbitrary classifications of historic and prehistoric so
that we can understand the distribution of population, and therefore
artifact, density.

The density of
artifact distribution is probably going to be a left skewed
distribution where the distribution falls off suddenly when lithic
technology is replaced with newer iron age technologies brought over
from Europe, or when population density is decimated by European
diseases.

We can assume that
the modality of the distribution of lithic artifacts will be around
the period of highest population density. When did Native Americans
first encounter Europeans and European diseases? Vikings? Columbus?
When did the population of the Americas begin to drop?

We can further
assume that the farther left of the modality the less probable the
discovery of artifacts is.

The farther we move
from the mean, or the modality, the less probable it will be that we
will find an artifact.

This implies that,
if we find an artifact, the artifact is within the higher
probabilities of the distribution of artifacts. In the case of a
skewed distribution a discovered prehistoric artifact is probably
between the mean, which will be on the left of the data point which
the artifact represents, and the modality, which will be to the right
of the data point the artifact represents.

This has some
interesting implications. Some data points have been discovered as
far back as 30-35 thousand years before present. Do we assume that
these data points are to the right or the left of the mean?
Chebychev’s Theorum describes the minimum probabilities of finding
a data point in non-Gaussian distributions, however, it is not as
easy to determine the probability of discovering a specific data
point within the distribution without understanding the shape of the
distribution.

Chebychev’s
Theorum allows us to say, for example, that the highest possible
probability of finding a data point between 2 and 3 standard
deviations on either side of the mean is about 14%. However, with a
left skewed distribution the probability of finding a data point to
the right of the mean is higher than the probability of finding an
artifact to the left of the mean.

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