36
Statistical Methods for Estimating Petroleum Resources
β ˆ = 0.5) when N = 400. The sample pool-size distribution (Fig. 3.6,
line C) is shown in the same fi gure for comparison. It is evident that the
mean and variance of the superpopulation pool-size distribution are
over- and underestimated, respectively, if the pools are assumed to be
randomly discovered (i.e., random sampling).
Lognormal/Nonparametric–Poisson Discovery Process Model
Previous Work
With the superpopulation concept, one can use a discrete probability distribution to express the number-of-pools distribution (Lee and
Wang, 1990). The total number of pools that exists in a population is
a value obtained from its superpopulation distribution. This section
presents a statistical method referred to as the Bayesian lognormal /
nonparametric–Poisson discovery process model (BDSCV) that is used
to estimate the superpopulation discrete number-of-pools distribution
Figure 3.5. Diagram showing relationships between log-likelihood value versus
the N value for the Beaverhill Lake play. LDSCV derived by the lognormal
discovery process method. NDSCV derived by the nonparametric discovery
process method.