More about Discovery Process Models
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From the results of these simulation studies, it can be concluded that
when the number of discoveries, n, increases, the impact of the shape of
a probability distribution diminishes. One can also conclude that the
mixture of two lognormal populations with different means and variances does not signifi cantly distort the estimation of N as sample size
increases. In addition, if a mixed population consists of various probability distributions, then NDSCV can be used, whereas LDSCV might
provide information about the N value as the sample size, n, increases.
Table 4.1. Summary of the Estimates for Various Populations When n = 30
(Lognormal Assumption Is Used)
Types of
populations
Total
resources
N
ˆ
N
ˆ
β
Upper percentiles
95
75
50
25
5
Lognormal
50,901 300 300 0.6 29,549 36,507 43,390 53,599
77,764
Weibull
6100 300 200 1.4
2231
2478
2682
2887
3246
Pareto
30,375 300 220 0.7
6958 13,000 22,533 45,569 183,400
Mixture
of two
lognormals
35,526 300 100 0.8
8974 14,884 21,952 34,633 88,884
Mixtures of
lognormal,
Weibull,
and Pareto
32,333 300 300 0.6 19,845 27,342 36,067 51,308
98,837
Table 4.2. Summary of the Estimates for Various Populations When n = 50
(Lognormal Assumption Is Used)
Types of
populations
Total
resources
N
ˆ
N
ˆ
β
Upper percentiles
95
75
50
25
5
Lognormal
50,901 300 300 0.6 42,921 51,586 59,560 70,796
95,843
Weibull
6100 300 400 1.0
5311
5729
6045
6391
6977
Pareto
30,375 300 300 0.7 14,547 20,714 28,149 41,694
87,147
Mixture
of two
lognormals
35,526 300 300 0.6 25,279 30,498 35,369 42,220
57,813
Mixtures of
lognormal,
Weibull,
and Pareto
32,333 300 300 0.6 16,114 21,871 28,568 39,927
74,302