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Non†parametric Estimation of the Number of Zeros in Truncated Count Distributions

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  • Pedro Puig
  • Célestin C. Kokonendji

Abstract

We present some lower bounds for the probability of zero for the class of count distributions having a log†convex probability generating function, which includes compound and mixed†Poisson distributions. These lower bounds allow the construction of new non†parametric estimators of the number of unobserved zeros, which are useful for capture†recapture models, or in areas like epidemiology and literary style analysis. Some of these bounds also lead to the well†known Chao's and Turing's estimators. Several examples of application are analysed and discussed.

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  • Pedro Puig & Célestin C. Kokonendji, 2018. "Non†parametric Estimation of the Number of Zeros in Truncated Count Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(2), pages 347-365, June.
    • Handle: RePEc:bla:scjsta:v:45:y:2018:i:2:p:347-365
    DOI: 10.1111/sjos.12293
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    Cited by:

    1. Kokonendji, Célestin C. & Puig, Pedro, 2018. "Fisher dispersion index for multivariate count distributions: A review and a new proposal," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 180-193.
    2. Orasa Anan & Dankmar Böhning & Antonello Maruotti, 2019. "On the Turing estimator in capture–recapture count data under the geometric distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 149-172, March.
    3. Puig, Pedro & Weiß, Christian H., 2020. "Some goodness-of-fit tests for the Poisson distribution with applications in Biodosimetry," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    4. Dankmar Böhning & Panicha Kaskasamkul & Peter G. M. Heijden, 2019. "A modification of Chao’s lower bound estimator in the case of one-inflation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(3), pages 361-384, April.
    5. Farcomeni, Alessio & Dotto, Francesco, 2021. "A correction to make Chao estimator conservative when the number of sampling occasions is finite," Statistics & Probability Letters, Elsevier, vol. 176(C).

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