See the odd-even formula in Fienberg 1972, or a localized version of it in Zwane 2004.
Matrix with column names corresponding to the possible capture patterns
The function is vectorized – it gets applied to each row of the input matrix, resulting in a vector of estimated rates of missingness or the total number missing
Fienberg SE (1972). "The Multiple Recapture Census for Closed Populations and Incomplete $2^k$ Contingency Tables." Biometrika, 59(3), pp. 591.
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