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On comparison of relative growth rates under different environmental conditions with application to biological data

Author

Listed:
  • Soumalya Mukhopadhyay

    (Visva Bharati University)

  • Arnab Hazra

    (Indian Statistical Institute)

  • Amiya Ranjan Bhowmick

    (Institute of Chemical Technology)

  • Sabyasachi Bhattacharya

    (Indian Statistical Institute)

Abstract

In this paper, we discuss a few empirical estimates of relative growth rate and their distributions based on two well-established parametric structures of the size variable- normal and log-normal with different growth curve models as the mean process. We discuss some exact and asymptotic testing procedures applicable to test the equality of expected relative growth rates over two or more different environmental situations, e.g. distinct geographical locations, several biological species, etc. Along with the tests under the parametric structures for the size variable, we consider some nonparametric tests as well. We perform tests for two other important hypotheses—whether the times taken to reach the maximum values of the relative growth rates are equal for all environments and whether those maximum values are equal. We illustrate our methods with two real life examples. The performances of the various testing procedures are studied by means of their power functions. Our methods have immense practical value in growth rate modeling in the biological context.

Suggested Citation

  • Soumalya Mukhopadhyay & Arnab Hazra & Amiya Ranjan Bhowmick & Sabyasachi Bhattacharya, 2016. "On comparison of relative growth rates under different environmental conditions with application to biological data," METRON, Springer;Sapienza Università di Roma, vol. 74(3), pages 311-337, December.
    • Handle: RePEc:spr:metron:v:74:y:2016:i:3:d:10.1007_s40300-016-0102-y
    DOI: 10.1007/s40300-016-0102-y
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    References listed on IDEAS

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    1. Zhiying Pan & D. Y. Lin, 2005. "Goodness-of-Fit Methods for Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 61(4), pages 1000-1009, December.
    2. Bhowmick, Amiya Ranjan & Saha, Bapi & Chattopadhyay, Joydev & Ray, Santanu & Bhattacharya, Sabyasachi, 2015. "Cooperation in species: Interplay of population regulation and extinction through global population dynamics database," Ecological Modelling, Elsevier, vol. 312(C), pages 150-165.
    3. Bratati Chakraborty & Sabyasachi Bhattacharya & Ayanendranath Basu & Subhadip Bandyopadhyay & Amit Bhattacharjee, 2014. "Goodness-of-fit testing for the Gompertz growth curve model," METRON, Springer;Sapienza Università di Roma, vol. 72(1), pages 45-64, April.
    4. Massimo Florio & Sara Colautti, 2005. "A logistic growth theory of public expenditures: A study of five countries over 100 years," Public Choice, Springer, vol. 122(3), pages 355-393, March.
    5. Young, William E. & Trent, Robert H., 1969. "Geometric Mean Approximations of Individual Security and Portfolio Performance*," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 4(2), pages 179-199, June.
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    Cited by:

    1. Chakraborty, Biman & Bhowmick, Amiya Ranjan & Chattopadhyay, Joydev & Bhattacharya, Sabyasachi, 2017. "Physiological responses of fish under environmental stress and extension of growth (curve) models," Ecological Modelling, Elsevier, vol. 363(C), pages 172-186.
    2. Kundu, Sayani & Dasgupta, Nirjhar & Chakraborty, Bratati & Paul, Ayan & Ray, Santanu & Bhattacharya, Sabyasachi, 2021. "Growth acceleration is the key for identifying the most favorable food concentration of Artemia sp," Ecological Modelling, Elsevier, vol. 455(C).

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