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Statistical Methods and Applications in Forestry and Environmental Sciences pp 213–230Cite as

Development in Copula Applications in Forestry and Environmental Sciences

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Part of the book series: Forum for Interdisciplinary Mathematics ((FFIM))

Abstract

Recently, copula is being used in social, natural, and physical sciences due to its flexibilities in joint distributions and marginals and high computing power. They are the powerful instruments to model-dependent structures between various complex correlated variables in environmental sciences. This chapter studies the development of copula models and its applications in the area of environmental sciences. It reviews the literature on the types of copula models, including Gumbel, Clayton, and vine, and outlines the theoretical development of mixture bivariate and multivariate copula distributions. A brief review of literature is done using DCC, ARCH, and GARCH copulas.

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Notes

  1. 1.

    Some of the material in this chapter is in a summarize form from a published review paper authored by Bhatti and Do (2019).

  2. 2.

    Archimedean copulas need to meet some varying criteria, for example, like convexity which are detailed in Nelsen (2007), Ahsanullah and Bhatti (2010), Al Rahahleh et al. (2017), Al Rahahleh and Bhatti (2017), Bhatti and Nguyen (2012), Nguyen and Bhatti (2012) and Nguyen et al. (2016).

  3. 3.

    Other measures of dependence have been used in the literature to compare copulas, such as the measures of concordance Kendall’s τ, Spearman’s ρ, and Gini’s co-graduation index. For further details, see Cherubini et al. (2004), Patton (2006) and Nelsen (2007).

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  1. Department of Economics and Finance, La Trobe University, Bundoora, VIC, 3083, Australia

    M. Ishaq Bhatti & Hung Quang Do

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  1. M. Ishaq Bhatti
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Correspondence to M. Ishaq Bhatti .

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  1. Indian Council of Forestry Research and Education, Dehradun, Uttarakhand, India

    Girish Chandra

  2. Indian Council of Forestry Research and Education, Dehradun, Uttarakhand, India

    Raman Nautiyal

  3. Indian Agricultural Statistics Research Institute, New Delhi, Delhi, India

    Hukum Chandra

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Bhatti, M.I., Do, H.Q. (2020). Development in Copula Applications in Forestry and Environmental Sciences. In: Chandra, G., Nautiyal, R., Chandra, H. (eds) Statistical Methods and Applications in Forestry and Environmental Sciences. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-1476-0_13

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