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Bayesian estimation of the number of species from Poisson-Lindley stochastic abundance model using non-informative priors

Author

Listed:
  • Anurag Pathak

    (Central University of Haryana)

  • Manoj Kumar

    (Central University of Haryana
    University of Delhi)

  • Sanjay Kumar Singh

    (Banaras Hindu University)

  • Umesh Singh

    (Banaras Hindu University)

  • Sandeep Kumar

    (Central University of Haryana
    GLA University)

Abstract

In this article, we propose a Poisson-Lindley distribution as a stochastic abundance model in which the sample is according to the independent Poisson process. Jeffery’s and Bernardo’s reference priors have been obtaining and proposed the Bayes estimators of the number of species for this model. The proposed Bayes estimators have been compared with the corresponding profile and conditional maximum likelihood estimators for their square root of the risks under squared error loss function (SELF). Jeffery’s and Bernardo’s reference priors have been considered and compared with the Bayesian approach based on biological data.

Suggested Citation

  • Anurag Pathak & Manoj Kumar & Sanjay Kumar Singh & Umesh Singh & Sandeep Kumar, 2024. "Bayesian estimation of the number of species from Poisson-Lindley stochastic abundance model using non-informative priors," Computational Statistics, Springer, vol. 39(7), pages 3881-3906, December.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:7:d:10.1007_s00180-024-01464-7
    DOI: 10.1007/s00180-024-01464-7
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    References listed on IDEAS

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    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. Leite, José G. & Rodrigues, Josemar & Milan, Luis A., 2000. "A Bayesian analysis for estimating the number of species in a population using nonhomogeneous Poisson process," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 153-161, June.
    3. Anne Chao & John Bunge, 2002. "Estimating the Number of Species in a Stochastic Abundance Model," Biometrics, The International Biometric Society, vol. 58(3), pages 531-539, September.
    4. Li-An Lin & Sheng Luo & Barry R. Davis, 2018. "Bayesian regression model for recurrent event data with event-varying covariate effects and event effect," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(7), pages 1260-1276, May.
    5. Anurag Pathak & Manoj Kumar & Sanjay Kumar Singh & Umesh Singh, 2022. "Statistical Inferences: Based on Exponentiated Exponential Model to Assess Novel Corona Virus (COVID-19) Kerala Patient Data," Annals of Data Science, Springer, vol. 9(1), pages 101-119, February.
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