= Lincoln-Petersen estimator
{c}
{title2=$\widehat N_{\mathrm{LP}}=MC/R$}
= Petersen estimator
{c}
{synonym}
The <Lincoln-Petersen estimator> is the <ratio estimator> obtained by matching the observed overlap to its <hypergeometric> <expected value>. It is defined when $R>0$. To distinguish that ratio from the exact <integer> maximization, consecutive positive <likelihoods> satisfy
$$
\frac{L(N+1)}{L(N)}
=\frac{(N+1-M)(N+1-C)}{(N+1)(N+1-M-C+R)}.
$$
This comparison is valid for $N\geq M+C-R$. For the toy counts, the numerator minus the denominator is $500-5(N+1)$. Thus the <likelihood function> increases up to ninety-nine, ties at ninety-nine and one hundred, then decreases for every larger <integer>. This independently establishes the global <maximum-likelihood estimates>, beyond the plotting window. The adjacent-ratio method is given in https://web.mit.edu/14.380/www/handouts/hypergeometric.pdf[Guiteras, §8].
Back to article page
