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For values of S < 10, this estimate is rough, and becomes extremely rough for values of S < 5. In the case where S = 0 (that is, there is no overlap at all) the
Lincoln Index is formally undefined. This can arise if the observers only find a small percentage of the
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The
Lincoln Index is merely an estimate. For example, the species in a given area could tend to be either very common or very rare, or tend to be either very hard or very easy to see. Then it would be likely that both observers would find a large share of the common species, and that both observers
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for estimating the total vocabulary of a language. Given two independent samples, the overlap between their vocabularies enables a useful estimate of how many more vocabulary items exist but did not happen to show up in either sample. A similar example involves estimating the number of typographical
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observers, then each observer clearly missed at least 95 species (that is, the 95 that only the other observer found). Thus, we know that both observers miss a lot. On the other hand, if 99 of the 100 species each observer found had been found by both, it is fair to expect that they have found a far
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actual species (perhaps by not looking hard enough or long enough), if the observers are using methods that are not statistically independent (for example if one looks only for large creatures and the other only for small), or in other circumstances.
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The
Lincoln Index formalizes this phenomenon. If E1 and E2 are the number of species (or words, or other phenomena) observed by two independent methods, and S is the number of observations in common, then the Lincoln Index is simply
63:. If some animals in a given area are caught and marked, and later a second round of captures is done: the number of marked animals found in the second round can be used to generate an estimate of the total population.
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Consider two observers who separately count the different species of plants or animals in a given area. If they each come back having found 100 species but only 5 particular species are found by
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would miss a large share of the rare ones. Such distributions would throw off the consequent estimate. Bagaimanapun, such distributions are unusual for natural phenomena, as suggested by
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T. Bohlin; B. Sundstrom (1977). "Influence of unequal catchability on population estimates using the
Lincoln and the removal method applied to electro-fishing".
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Petersen, C. G. J. (1896). "The Yearly
Immigration of Young Plaice Into the Limfjord From the German Sea",
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T. J. Gaskell and B. J. George propose an enhancement of the
Lincoln Index that claims to reduce bias.
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T. J. Gaskell; B. J. George (1972). "A Bayesian
Modification of the Lincoln Index".
199:. Circular. Vol. 118. Washington, DC: United States Department of Agriculture
268:"Estimating Population Sizes by Mark-recapture and Removal Sampling Methods"
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Calculating
Waterfowl Abundance on the Basis of Banding Returns
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higher percentage of the total species that are there to find.
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errors remaining in a text, from two proofreaders' counts.
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the population size of an animal species. Described by
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23:is a statistical measure used in several fields to
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213:Report of the Danish Biological Station (1895)
253:Southwood, T.R.E. & Henderson, P. (2000)
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31:in 1930, it is also sometimes known as the
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130:{\displaystyle L={E_{1}E_{2} \over S}.}
39:who was the first to use the related
257:, 3rd edn. Blackwell Science, Oxford.
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193:Lincoln, Frederick C. (May 1930).
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59:The same reasoning applies to
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221:Journal of Applied Ecology
66:Another example arises in
303:Gaskell and George (1972)
68:computational linguistics
29:Frederick Charles Lincoln
330:Environmental statistics
181:Inter-rater reliability
33:Lincoln-Petersen method
270:. University of Texas.
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37:C.G. Johannes Petersen
320:Ecological techniques
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176:German tank problem
16:Statistical measure
325:Estimation methods
255:Ecological Methods
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61:mark and recapture
41:mark and recapture
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187:Further reading
166:Sampling Theory
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201:. Retrieved
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47:Applications
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144:Limitations
75:Formulation
314:Categories
215:, 6, 5–84.
151:Zipf's Law
160:See also
43:method.
25:estimate
291:3543331
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203:21 May
35:after
287:JSTOR
283:OIKOS
241:Notes
205:2013
53:both
19:The
229:doi
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225:9
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120:S
114:2
110:E
104:1
100:E
93:=
90:L
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