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Just a note

Even when its assumptions are fully met, where the sample size is small, this statistic provides a (statistically) biased estimate of population size.

To allow for this Bailey published a less biased estimator in 1951, namely:

= [r(n+1)]/[m+1]

along with a formula to estimate its random variation.

Unfortunately, the error resulting from failure to meet the assumptions of the model is usually much greater than any bias resulting from a small sample size.