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Appendix B
If
2. n 5 N, the estimator is also reduced to Equation B.2. This
is because all the members have been observed from the fi nite
population, and thus the sampling design itself is irrelevant. If
all members of the fi nite population have been observed, then
the best estimator of F is, of course, the usual edf estimator.
If
3.
N → ∞ with fi xed n, it can be shown that ˆ k
p ∝ n k / z k , the
length-biased sampling estimator given by Cox (1969) (see
Appendix A).
When w(
4.
z k ) is large, the second term in Equation B.5 is small
and so ˆ k
p 5 n k / N, implying that all the members in the fi nite
population have, in fact, been discovered.
After ˆ
F has been estimated, it is then considered to be the population
distribution. Bootstrapped samples are randomly drawn from ˆ
F to
obtain a sample of size N. A sample of size n is simulated by the discovery process model with exploration effi ciency b, which is also estimated
from the nonparametric model. The m and s
2 are estimated from sample
size n using the anchored method (Kaufman, 1986) (see Appendix A).
These two sampling steps are repeated 5000 times. Standard deviations
of m and s
2 are computed and their 95% intervals are then derived.