IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i8p761-d259031.html
   My bibliography  Save this article

Understanding the Evolution of Tree Size Diversity within the Multivariate Nonsymmetrical Diffusion Process and Information Measures

Author

Listed:
  • Petras Rupšys

    (Agriculture Academy, Vytautas Magnus University, Universiteto g. 20-214, 53361 LT Akademija, Kaunas District, Lithuania)

Abstract

This study focuses on the stochastic differential calculus of Itô, as an effective tool for the analysis of noise in forest growth and yield modeling. Idea of modeling state (tree size) variable in terms of univariate stochastic differential equation is exposed to a multivariate stochastic differential equation. The new developed multivariate probability density function and its marginal univariate, bivariate and trivariate distributions, and conditional univariate, bivariate and trivariate probability density functions can be applied for the modeling of tree size variables and various stand attributes such as the mean diameter, height, crown base height, crown width, volume, basal area, slenderness ratio, increments, and much more. This study introduces generalized multivariate interaction information measures based on the differential entropy to capture multivariate dependencies between state variables. The present study experimentally confirms the effectiveness of using multivariate interaction information measures to reconstruct multivariate relationships of state variables using measurements obtained from a real-world data set.

Suggested Citation

  • Petras Rupšys, 2019. "Understanding the Evolution of Tree Size Diversity within the Multivariate Nonsymmetrical Diffusion Process and Information Measures," Mathematics, MDPI, vol. 7(8), pages 1-22, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:761-:d:259031
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/8/761/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/8/761/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Clive W.J. Granger, 2004. "Time Series Analysis, Cointegration, and Applications," American Economic Review, American Economic Association, vol. 94(3), pages 421-425, June.
    2. William McGill, 1954. "Multivariate information transmission," Psychometrika, Springer;The Psychometric Society, vol. 19(2), pages 97-116, June.
    3. Joe, Harry, 2008. "Accuracy of Laplace approximation for discrete response mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5066-5074, August.
    4. Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2019. "A Note on Estimation of Multi-Sigmoidal Gompertz Functions with Random Noise," Mathematics, MDPI, vol. 7(6), pages 1-18, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:hig:wpaper:98sti2019 is not listed on IDEAS
    2. Petersen, Alexander M. & Rotolo, Daniele & Leydesdorff, Loet, 2016. "A triple helix model of medical innovation: Supply, demand, and technological capabilities in terms of Medical Subject Headings," Research Policy, Elsevier, vol. 45(3), pages 666-681.
    3. Park, Han Woo & Leydesdorff, Loet, 2010. "Longitudinal trends in networks of university-industry-government relations in South Korea: The role of programmatic incentives," Research Policy, Elsevier, vol. 39(5), pages 640-649, June.
    4. Songyot Nakariyakul, 2019. "A hybrid gene selection algorithm based on interaction information for microarray-based cancer classification," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-17, February.
    5. Louis Verny & Nadir Sella & Séverine Affeldt & Param Priya Singh & Hervé Isambert, 2017. "Learning causal networks with latent variables from multivariate information in genomic data," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-25, October.
    6. Delis, Manthos D. & Karavias, Yiannis, 2015. "Optimal versus realized bank credit risk and monetary policy," Journal of Financial Stability, Elsevier, vol. 16(C), pages 13-30.
    7. Björn Andersson & Tao Xin, 2021. "Estimation of Latent Regression Item Response Theory Models Using a Second-Order Laplace Approximation," Journal of Educational and Behavioral Statistics, , vol. 46(2), pages 244-265, April.
    8. Xiaojun Hu & Xian Li & Ronald Rousseau, 2021. "Mathematical reflections on Triple Helix calculations," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(10), pages 8581-8587, October.
    9. Jean Loo & Haihong He, 2018. "Economic Growth and Government Debt of Six Large National Economies before and after the 2008 Financial Crisis," Accounting and Finance Research, Sciedu Press, vol. 7(4), pages 1-30, November.
    10. Inga A. Ivanova & Loet Leydesdorff, 2014. "A simulation model of the Triple Helix of university–industry–government relations and the decomposition of the redundancy," Scientometrics, Springer;Akadémiai Kiadó, vol. 99(3), pages 927-948, June.
    11. Loet Leydesdorff & Han Woo Park & Balazs Lengyel, 2014. "A routine for measuring synergy in university–industry–government relations: mutual information as a Triple-Helix and Quadruple-Helix indicator," Scientometrics, Springer;Akadémiai Kiadó, vol. 99(1), pages 27-35, April.
    12. Karl, Andrew T. & Yang, Yan & Lohr, Sharon L., 2014. "Computation of maximum likelihood estimates for multiresponse generalized linear mixed models with non-nested, correlated random effects," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 146-162.
    13. Adriana AnaMaria DAVIDESCU & Catalin Corneliu GHINARARU, 2015. "The Hare and the Tortoise. How Older Generations Are Replaced By Young One on the Labour Market: Signals and Insights from the Relationship between Shadow Economy and Active Ageing," Economia. Seria Management, Faculty of Management, Academy of Economic Studies, Bucharest, Romania, vol. 18(1), pages 163-171, June.
    14. Lengyel, Balázs & Leydesdorff, Loet, 2015. "The Effects of FDI on Innovation Systems in Hungarian Regions: Where is the Synergy Generated?," MPRA Paper 73945, University Library of Munich, Germany.
    15. Heagney, E.C. & Falster, D.S. & Kovač, M., 2021. "Land clearing in south-eastern Australia: Drivers, policy effects and implications for the future," Land Use Policy, Elsevier, vol. 102(C).
    16. Sven Baehre & Michele O’Dwyer & Lisa O’Malley & Nick Lee, 2022. "The use of Net Promoter Score (NPS) to predict sales growth: insights from an empirical investigation," Journal of the Academy of Marketing Science, Springer, vol. 50(1), pages 67-84, January.
    17. Han Woo Park, 2014. "Mapping election campaigns through negative entropy: Triple and Quadruple Helix approach to South Korea’s 2012 presidential election," Scientometrics, Springer;Akadémiai Kiadó, vol. 99(1), pages 187-197, April.
    18. Minjeong Jeon & Sophia Rabe-Hesketh, 2012. "Profile-Likelihood Approach for Estimating Generalized Linear Mixed Models With Factor Structures," Journal of Educational and Behavioral Statistics, , vol. 37(4), pages 518-542, August.
    19. Genovaitė Liobikienė & Mindaugas Butkus & Kristina Matuzevičiūtė, 2019. "The Contribution of Energy Taxes to Climate Change Policy in the European Union (EU)," Resources, MDPI, vol. 8(2), pages 1-23, April.
    20. Siti Nur Zahara HAMZAH & Evan LAU, 2013. "The role of social factors in explaining crime," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(6(583)), pages 99-118, June.
    21. Loet Leydesdorff & Igone Porto-Gomez, 2019. "Measuring the expected synergy in Spanish regional and national systems of innovation," The Journal of Technology Transfer, Springer, vol. 44(1), pages 189-209, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:761-:d:259031. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.