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Completely monotone distributions: Mixing, approximation and estimation of number of species

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  • Balabdaoui, Fadoua
  • Kulagina, Yulia

Abstract

The problem of species richness estimation using complete monotonicity of the distribution of species abundances is considered. Complete monotonicity is the most natural surrogate for k-monotonicity when k is large. The latter model has been considered in the same estimation problem adopting two different approaches which both necessitate selecting the unknown degree of monotonicity k via some chosen criterion. It is shown that such selection procedures can be avoided by appropriately approximating the true completely monotone distribution by a kn-monotone one such that kn grows logarithmically as a function of the sample size n. Furthermore, the proposed estimator of the true total number of species is proved to be asymptotically normal. An extended simulation study indicates that it is quite competitive when compared to other available estimators, and this remains true even when complete monotonicity is not satisfied. It is further illustrated how the method can be applied in practice by using four real datasets.

Suggested Citation

  • Balabdaoui, Fadoua & Kulagina, Yulia, 2020. "Completely monotone distributions: Mixing, approximation and estimation of number of species," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:csdana:v:150:y:2020:i:c:s0167947320301055
    DOI: 10.1016/j.csda.2020.107014
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