An important problem associated with the above theory is the construction of a confidence interval for N. In earlier work, a natural approach to interval estimation was to assume that N^ was asymptotically normal and use N^± 1.96 standard errors. Unfortunately the distribution of N^ is skewed in practice and the above interval can give misleading results. To get around this we might try and find a suitable transformation of which would make it look more like a normal random variable. For example Burnham (see Chao(1)) proposed using log( N^- r), where r is the number of different animals caught (i.e. the number of different people on all the lists). However, instead of trying to find a suitable transformation of N^, which is essentially equivalent to reparameterising the model, one can use a likelihood profile to construct a confidence interval (2,3). One advantage of using such an interval is that the likelihood function is the same irrespective of whether one works with N or some transformation such as LogN. Using this approach is like working with the best possible transformation of N^.

Another approach is to get the computer to work for you and use the so-called bootstrap method for numerically finding a confidence interval. This approach, pioneered by Buckland in capture-recapture (see model selection section), uses simulation to generate distributions.

1. Chao A. Estimating population size for sparse data in capture-recapture experiments. Biometrics 1989;45:427-438.

2. Cormack RM. Interval estimation for mark-recapture studies of closed populations. Biometrics 1992;48:567-576.

3. Regal RR and Hook EB. Goodness-of-fit based confidence intervals for estimates of the size of a closed population. Stat. Med. 1984;3:287-291.