but is biased at small sample sizes. An alternative less biased estimator of population size is given by the Chapman estimator: Sample calculation The example (n, K, k) = (10, 15, 5) gives Note that the answer provided by this equation must be truncated not rounded. Thus, the Chapman method estimates 28 turtles in the lake. Surprisingly, Chapman's estimate was one conjecture from a range of possible estimators: "In practice, the whole number immediately less than (K+1)(n+1)/(k+1) or even Kn/(k+1) will be the estimate. The above form is more convenient for mathematical purposes."(see footnote, page 144). Chapman also found the estimator could have considerable negative bias for small Kn/N (page 146), but was unconcerned because the estimated standard deviations were large for these cases. Confidence interval An approximate confidence interval for the population size N can be obtained as: where corresponds to the quantile of a standard normal random variable, and The example (n, K, k) = (10, 15, 5) gives the estimate N ≈ 30 with a 95% confidence interval of 22 to 65. It has been shown that this confidence interval has actual coverage probabilities that are close to the nominal level even for small populations and extreme capture probabilities (near to 0 or 1), in which cases other confidence intervals fail to achieve the nominal coverage levels. Bayesian estimate The mean value ± standard deviation is where for for A derivation is found here: Talk:Mark and recapture#Statistical treatment. The example (n, K, k) = (10, 15, 5) gives the estimate N ≈ 42 ± 21.5 Capture probability The capture probability refers to the probability of a detecting an individual animal or person of interest, and has been used in both ecology and epidemiology for detecting animal or human diseases, respectively. The capture probability is often defined as a two-variable model, in which f is defined as the fraction of a finite resource devoted to detecting the animal or person of interest from a high risk sector of an animal or human population, and q is the frequency of time that the problem (e.g., an animal disease) occurs in the high-risk versus the low-risk sector. For example, an application of the model in the 1920s was to detect typhoid carriers in London, who were either arriving from zones with high rates of tuberculosis (probability q that a passenger with the disease came from such an area, where q>0.5),