A new estimator for the number of species in a population

Lorenzo Cecconi, Alberto Gandolfi, Chelluri C.A. Sastri

    Research output: Contribution to journalArticle

    Abstract

    We consider the classic problem of estimating T, the total number of species in a population, from repeated counts in a simple random sample. We first show that the frequently used Chao-Lee estimator can in fact be obtained by Bayesian methods with a Dirichlet prior, and then use such clarification to develop a new estimator; numerical tests and some real experiments show that the new estimator is more flexible than existing ones, in the sense that it adapts to changes in the normalized interspecies variance γ2. Our method involves simultaneous estimation of T, γ2, and of the parameter λ in the Dirichlet prior, and the only limitation seems to come from the required convergence of the prior which imposes the restriction γ2 ≤ 1. We also obtain confidence intervals for T and an estimation of the species’ distribution. Some numerical examples are given, together with applications to sampling from a Census database closely following Benford’s law, showing good performances of the new estimator, even beyond γ2 = 1. Tests on confidence intervals show that the coverage frequency appears to be in good agreement with the desired confidence level.

    Original languageEnglish (US)
    Pages (from-to)80-100
    Number of pages21
    JournalSankhya A
    Volume74
    Issue number1
    DOIs
    StatePublished - Feb 1 2012

    Fingerprint

    Dirichlet Prior
    Estimator
    Confidence interval
    Simultaneous Estimation
    Census
    Confidence Level
    Bayesian Methods
    Count
    Coverage
    Restriction
    Numerical Examples
    Experiment
    Dirichlet
    Confidence
    Data base
    Bayesian methods
    Sampling

    ASJC Scopus subject areas

    • Statistics, Probability and Uncertainty
    • Statistics and Probability

    Cite this

    Cecconi, L., Gandolfi, A., & Sastri, C. C. A. (2012). A new estimator for the number of species in a population. Sankhya A, 74(1), 80-100. https://doi.org/10.1007/s13171-012-0012-x

    A new estimator for the number of species in a population. / Cecconi, Lorenzo; Gandolfi, Alberto; Sastri, Chelluri C.A.

    In: Sankhya A, Vol. 74, No. 1, 01.02.2012, p. 80-100.

    Research output: Contribution to journalArticle

    Cecconi, L, Gandolfi, A & Sastri, CCA 2012, 'A new estimator for the number of species in a population', Sankhya A, vol. 74, no. 1, pp. 80-100. https://doi.org/10.1007/s13171-012-0012-x
    Cecconi, Lorenzo ; Gandolfi, Alberto ; Sastri, Chelluri C.A. / A new estimator for the number of species in a population. In: Sankhya A. 2012 ; Vol. 74, No. 1. pp. 80-100.
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