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Nonparametric estimation of species richness using discrete k-monotone distributions

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  • Chee, Chew-Seng
  • Wang, Yong

Abstract

Nonparametric mixture models are commonly used to estimate the number of unobserved species for their robustness of modelling heterogeneity. In particular, Poisson mixtures are popular in this regard, but they are also known to have the boundary problem that causes unstable estimation. A family of shape-restricted distributions known as discrete k-monotone distributions is proposed for species richness estimation. These distributions are in fact also nonparametric mixtures and can thus be fitted rapidly via some algorithms that are made available recently. As shown by empirical studies, as compared with Poisson mixtures, their use avoids the boundary problem and gives more stable and more accurate estimates.

Suggested Citation

  • Chee, Chew-Seng & Wang, Yong, 2016. "Nonparametric estimation of species richness using discrete k-monotone distributions," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 107-118.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:107-118
    DOI: 10.1016/j.csda.2014.10.021
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    References listed on IDEAS

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    1. Dankmar Böhning & Ronny Kuhnert, 2006. "Equivalence of Truncated Count Mixture Distributions and Mixtures of Truncated Count Distributions," Biometrics, The International Biometric Society, vol. 62(4), pages 1207-1215, December.
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    6. Yong Wang, 2007. "On fast computation of the non‐parametric maximum likelihood estimate of a mixing distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 185-198, April.
    7. repec:dau:papers:123456789/4650 is not listed on IDEAS
    8. Wang, Ji-Ping Z. & Lindsay, Bruce G., 2005. "A Penalized Nonparametric Maximum Likelihood Approach to Species Richness Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 942-959, September.
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    Cited by:

    1. Giguelay, J. & Huet, S., 2018. "Testing k-monotonicity of a discrete distribution. Application to the estimation of the number of classes in a population," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 96-115.
    2. Balabdaoui, Fadoua & Kulagina, Yulia, 2020. "Completely monotone distributions: Mixing, approximation and estimation of number of species," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
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    4. Balabdaoui, Fadoua & Durot, Cécile & Koladjo, Babagnidé François, 2018. "Testing convexity of a discrete distribution," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 8-13.

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