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Statistical Methods for Estimating Petroleum Resources
If a data set were a random sample from its population, then E[•] and
N!/(N – n)! would be omitted from the likelihood function. That is to
say, a random sample does not contain the information relating to the
value of total number of pools in the play.
The contribution of the Kaufman model is that it not only characterizes the nature of the exploration process by setting the two basic
assumptions, but it also expresses the likelihood function for the question: What is the probability of a pool with size x being deposited and
also discovered at a certain point in the discovery sequence? Although
it is true that this question is not of importance to explorationists, it
does lead us to establish the likelihood function containing information on the superpopulation lognormal pool-size distribution and
the total number of pools, N. Furthermore, the lognormal assumption
has been used, but the model can handle all types of probability distributions. However, each probability distribution requires a specifi c
Figure 3.4. Diagram illustrating geological meanings of the lognormal
discovery model.