Journal Article10.1080/01621459.1992.10475194
Estimating the Number of Classes via Sample Coverage
Anne Chao,Shen-Ming Lee +1 more
1.3K
TL;DR: This work generalizes the result of Esty to a nonparametric approach and extends Darroch and Ratcliff to incorporate the heterogeneity of the class probabilities to play an important role in the recommended estimation procedures.
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Abstract: Assume that a random sample is drawn from a population with unknown number of classes and possibly unequal class probabilities. A nonparametric estimation technique is proposed to estimate the number of classes using the idea of sample coverage, which is defined as the sum of the cell probabilities of the observed classes. Since expected sample coverage can be well estimated, we were motivated to find its role in the estimation of the number of classes. This work generalizes the result of Esty to a nonparametric approach and extends Darroch and Ratcliff to incorporate the heterogeneity of the class probabilities. The coefficient of variation of the class sizes is shown to play an important role in the recommended estimation procedures. The performance of the proposed estimators is investigated by means of Monte Carlo simulations.
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References
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Nonparametric estimation of the number of classes in a population
TL;DR: On applique la methode d'Efron (1981, 1982) a la construction d'intervalles de confiance bases sur des distributions du bootstrap as discussed by the authors.
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The Relation Between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population
TL;DR: It is shown that in a large collection of Lepidoptera captured in Malaya the frequency of the number of species represented by different numbers of individuals fitted somewhat closely to a hyperbola type of curve, so long as only the rarer species were considered.
Estimating the population size for capture-recapture data with unequal catchability.
TL;DR: A point estimator and its associated confidence interval for the size of a closed population are proposed under models that incorporate heterogeneity of capture probability andumerical results show that the proposed confidence interval performs satisfactorily in maintaining the nominal levels.
2.4K
The number of new species, and the increase in population coverage, when a sample is increased
I. J. Good,G. H. Toulmin +1 more
TL;DR: In this paper, a sample of size N is drawn at random from a population of animals of various species, and methods are given for estimating, knowing only the contents of this sample, the number of species which will be represented r times in a second sample of N of size AN; these also enable us to estimate the proportion of different species and the whole population represented in the second sample.
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