A Mixture of Clayton, Gumbel, and Frank Copulas: A Complete Dependence Model

Boateng, Maxwell Akwasi; Omari-Sasu, Akoto Yaw; Avuglah, Richard Kodzo; Frempong, Nana Kena

doi:10.1155/2022/1422394

Cited by 7 publications

(6 citation statements)

References 17 publications

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“…The dependence parameters (θ) associated with the Clayton copula were determined to be 1.7086, 1.0440, and 3.0970 for the "precipitation-mean temperature copula," "precipitation-maximum temperature copula," and "precipitation-minimum temperature copula," respectively (Table 5). Notably, these parameters deviated signi cantly from the independence coe cient of this copula, which is conventionally set at 0 (Boateng et al, 2022). The positive dependence parameters seen in each case indicate the presence of signi cant interdependence between the respective pairs of variables.…”

Section: Copula Resultsmentioning

confidence: 94%

Interdependency analysis between Precipitation and Temperature in Bangladesh: A copula-based approach

Prodhan,

Islam

2024

Preprint

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Climate change presents a significant challenge to global ecosystems and human well-being, primarily through alterations in temperature and precipitation patterns. Understanding the interdependence between these crucial climatic parameters is crucial for assessing the impacts of climate change, particularly on extreme events like floods and droughts. This study employed copula functions to model the joint distribution of temperature and precipitation, surpassing their individual marginal distributions. The findings revealed strong correlations, as indicated by Kendall's tau coefficients and Spearman's rank correlation coefficients, between precipitation and mean temperature (τ = 0.524, ρ = 0.7), precipitation and maximum temperature (τ = 0.306, ρ = 0.456), and precipitation and minimum temperature (τ = 0.645, ρ = 0.795) at the 1% level of significance. Precipitation and minimum temperature both showed a marginal distribution of generalized Pareto, whereas mean temperature and maximum temperature showed marginal distributions of generalized extreme value and Weibull, respectively. Despite differing marginal distributions, copula modeling enables the establishment of a joint distribution. Among the copula functions tested, the Clayton copula emerges as the most suitable, exhibiting minimal AIC, BIC, RMSE, and maximal log-likelihood (LL) for all temperature (mean, maximum, and minimum) types. Overall, this study emphasizes the utility of copula-based approaches in analyzing the complex interdependence of climatic variables and their implications for climate change assessment and extreme event analysis.

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Section: Copula Resultsmentioning

confidence: 94%

Interdependency analysis between Precipitation and Temperature in Bangladesh: A copula-based approach

Prodhan,

Islam

2024

Preprint

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“…Patient 18 (good tracker) with a WPB% of 93.8% and patient 28 (poor tracker) with WPB% of 50.8% (Table 3) were studied in detail in [20,21], for which both upper and lower tails/thresholds of over or under-estimation of agitation levels by the nurses' rating were established using copula dependence analytics (see also [27][28][29]).…”

Section: Tablementioning

confidence: 99%

“…Parametric copula families are conventionally constructed to satisfy different combinations of bivariate dependence structures with tail behaviours [28]. The general definition of Archimedean copulas is given by Boateng [29]. It is noteworthy that the Clayton, Gumbel, and Frank copulas are examples of existing Archimedean copulas.…”

Section: Copula Formulationmentioning

confidence: 99%

“…It is noteworthy that the Clayton, Gumbel, and Frank copulas are examples of existing Archimedean copulas. A discussion about the Clayton, Gumbel, and Frank copulas, and tail dependence of a bivariate copula, Kendall's tau representations, and copula models of the Clayton, Frank, and Gumbel copulas are also defined in [29]. The Clayton copula, for example, accommodates only lower tail dependence [30], the Frank copula allows dependence around the mode [31], and the Gumbel is relevant only when upper tail dependence exists [32].…”

Section: Copula Formulationmentioning

confidence: 99%

“…The visuals in Section 3 of this chapter illustrate these trends. We refer the reader to Boeting [29] and below give the bivariate Gaussian formulation and bivariate Frank and Gumbel copula, as three examples.…”

Section: Copula Formulationmentioning

confidence: 99%

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Copula Modelling of Agitation-Sedation (A-S) in ICU: Threshold Analysis of Nurses’ Scores of A-S and Automated Drug Infusions by Protocol

Hudson¹,

Tursunalieva²,

Chase³

2022

Recent Advances in Medical Statistics

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Pain management is increasingly recognised as a formal medical subspecialty worldwide. Empirical distributions of the nurses’ ratings of a patient’s pain and/or agitation levels and the administered dose of sedative are often positively skewed, and if the joint distribution is non-elliptical, then high nurses’ ratings of a patient’s agitation levels may not correspond to the true occurrences of patient’s agitation-sedation (A-S). Copulas are used to capture such nonlinear dependence between skewed distributions and check for the presence of lower (LT) and/or upper tail (UT) dependence between the nurses’ A-S rating and the automated sedation dose, thus finding thresholds and regions of mismatch between the nurse’s scores and automated sedation dose, thereby suggesting a possible way forward for an improved alerting system for over- or under-sedation. We find for LT dependence nurses tend to underestimate the patient’s agitation in the moderate agitation zone. In the mild agitation zone, nurses tend to assign a rating, that is, on average, 0.30 to 0.45 points lower than expected for the patient’s given agitation severity. For UT dependence in the moderate agitation zone, nurses tend to either moderately or strongly underestimate patient’s agitation, but in periods of severe agitation, nurses tend to overestimate a patient’s agitation. Our approach lends credence to augmenting conventional RASS and SAS agitation measures with semi-automated systems and identifying thresholds and regions of deviance for alerting increased risk.

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Interdependency analysis between precipitation and temperature in Bangladesh: a copula-based approach

Prodhan,

Islam

2024

Theor Appl Climatol

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A Mixture of Clayton, Gumbel, and Frank Copulas: A Complete Dependence Model

Cited by 7 publications

References 17 publications

Interdependency analysis between Precipitation and Temperature in Bangladesh: A copula-based approach

Interdependency analysis between Precipitation and Temperature in Bangladesh: A copula-based approach

Copula Modelling of Agitation-Sedation (A-S) in ICU: Threshold Analysis of Nurses’ Scores of A-S and Automated Drug Infusions by Protocol

Interdependency analysis between precipitation and temperature in Bangladesh: a copula-based approach

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