The statistical paleontology of Charles Lyell and the coupon problem

Lyell, a founder of the science of geology, used statistical models to describe the changes that had occurred in the earth and its environment. From this model he attempted to, establish a time frame for each epoch, This article shows that Lyell's model is equivalent to the classic coupon problem included in many probability texts. Furthermore, it is shown that the time frame deduced by Lyell is inconsistent with the model he was using. The proper time frame consistent with the model is provided. A second model that was considered by Lyell is also investigated.