 Chapman estimator

The Chapman estimator is a correction intended to reduce the small-sample bias of the Lincoln-Petersen estimator. Under the fixed-size hypergeometric sampling assumptions it is exactly an unbiased estimator when $M+C\ge N$; it can have nonzero bias otherwise. This qualification and the formula are stated in Barker, §1.1.1, equation (1.3), citing Chapman's work through Seber. For the toy observations,It is an alternative estimator, not a maximum-likelihood estimate for this capture-recapture model. The Chapman estimator remains finite when $R=0$, but a finite output does not supply the missing overlap information or repair unequal catchability, lost marks, or population change.