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Abstract:
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It is well known that logit confidence intervals for the odds ratio are acceptable for small samples unless the true odds ratio is very large. In single capture-recapture estimation the odds ratio equals to 1. Thus, a transformation of the logit confidence intervals for the odds ratio is proposed in order to estimate the size of a closed population under single capture-recapture. It is found that the logit-based interval, resulting to add .5 to each observed count before computation, has actual coverage probabilities near to the nominal level even for small populations and even for capture probabilities near to 0 or 1, which is not guaranteed for other intervals proposed in statistical literature. Thus, given that the .5 logit-based interval is very simple to compute and has a good performance, it is appropriated to be implemented for most of the users of capture-recapture methods.
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