Copula Modeling: An Introduction for Practitioners

Trivedi, Pravin K.; Zimmer, David M.

doi:10.1561/0800000005

Cited by 546 publications

(510 citation statements)

References 27 publications

(36 reference statements)

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“…Microbes interact with their hosts and their communities, and these interactions have been implicated in numerous human health conditions including obesity and metabolic syndrome (Ley et al, 2005;Turnbaugh et al, 2009;Vrieze et al, 2012;Ridaura et al, 2013), cardiovascular disease (Wang et al, 2011), Clostridium difficile colitis (Gough et al, 2011), inflammatory bowel diseases (Gevers et al, 2014) and HIV (Lozupone et al, 2013a). These communities are influenced by diet, culture, geography, age and antibiotic use, among other factors (Lozupone et al, 2013b), and are also very important in other systems, such as soils, lakes and oceans (Chaffron et al, 2010;Beman et al, 2011;Steele et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Correlation detection strategies in microbial data sets vary widely in sensitivity and precision

et al. 2016

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Disruption of healthy microbial communities has been linked to numerous diseases, yet microbial interactions are little understood. This is due in part to the large number of bacteria, and the much larger number of interactions (easily in the millions), making experimental investigation very difficult at best and necessitating the nascent field of computational exploration through microbial correlation networks. We benchmark the performance of eight correlation techniques on simulated and real data in response to challenges specific to microbiome studies: fractional sampling of ribosomal RNA sequences, uneven sampling depths, rare microbes and a high proportion of zero counts. Also tested is the ability to distinguish signals from noise, and detect a range of ecological and time-series relationships. Finally, we provide specific recommendations for correlation technique usage. Although some methods perform better than others, there is still considerable need for improvement in current techniques.

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Section: Introductionmentioning

confidence: 99%

Correlation detection strategies in microbial data sets vary widely in sensitivity and precision

et al. 2016

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“…Suppose that a random vector has a joint distribution function with continuous marginal distribution function that has uniform distribution, then there exists a unique d-dimensional copula. In this section, the theory that is the central foundation of the copula is described (Genest and McKay, 1986;Joe, 2015;Nelsen, 2016;Sklar, 1959;Trivedi and Zimmer, 2005).…”

Section: Copula Functionmentioning

confidence: 99%

Copula modelling for multivariate statistical process control: a review

Busababodhin

Amphanthong

2016

CSAM

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Modern processes often monitor more than one quality characteristic that are referred to as multivariate statistical process control (MSPC) procedures. The MSPC is the most rapidly developing sector of statistical process control and increases interest in the simultaneous inspection of several related quality characteristics. Most multivariate detection procedures based on a multi-normality assumptions are independent, but there are many processes that assume non-normality and correlation. Many multivariate control charts have a lack of related joint distribution. Copulas are tool to construct multivariate modelling and formalizing the dependence structure between random variables and applied in several fields. From copula literature review, there are a few copula to apply in MSPC that have multivariate control charts, and represent a successful tool to identify an out-of-control process. This paper presents various types of copulas modelling for the multivariate control chart. The performance measures of the control chart are the average run length (ARL) and the average number of observations to signal (ANOS). Furthermore, a Monte Carlo simulation is shown when the observations were from an exponential distribution.

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“…where the copula function, C, takes the margins ( ) F x and ( ) G n as arguments but the function itself is independent of these margins, and where θ is a dependence parameter; see for instance Trivedi and Zimmer (2005). Thus, in contrast to some other contributions in the HI literature, such as King (1983) and Jenkins (1988), for instance, where the "benchmarking" is done by constructing artificial The Appendix contains a description of the data we have used to estimate the copulas.…”

Section: The Measurement Of Hi Using Copulasmentioning

confidence: 99%

Horizontal inequity under a dual income tax system: principles and measurement

Bø

Lambert

Thoresen

2011

Int Tax Public Finance

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Abstract:Tax systems with separate taxation of wage and capital income, also called dual income tax systems, have gained relevance through the Mirrlees Review. Obviously, such tax systems are exposed to horizontal equity (HE) failures, or horizontal inequity (HI). HE and HI have a firm grip on assessment of fair tax policies, both from an academic point of view and in general public debate. The dual income tax system of Norway was modified by the tax reform of 2006 precisely because the previous schedule failed to deliver equal tax treatment of equals. This paper discusses the meaning and measurement of HI effects of dual income tax systems, and evaluates the development of HI for Norway over the time period 2000-2008 using micro data. A copula-based identification strategy efficiently establishes a framework for evaluations of HI over time. The dual income tax system and the early announcement of its impending revision during the period under examination created measurement problems which we had to account for by defining a new income concept for the empirical strategy. As expected, we find less HI in Norway after the reform of 2006. Keywords: Dual income tax, Horizontal inequity, Reranking, Copula estimation JEL classification: D31, D63, H31Acknowledgements: This work is part of the evaluation of the Norwegian tax reform of 2006, initiated and sponsored by the Norwegian Ministry of Finance. We thank Erik Fjaerli and Elin Halvorsen for their help establishing the data set that is used in this study. We thank Erling Holmøy for comments to an earlier version of the paper.

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Copula Modeling: An Introduction for Practitioners

Cited by 546 publications

References 27 publications

Correlation detection strategies in microbial data sets vary widely in sensitivity and precision

Correlation detection strategies in microbial data sets vary widely in sensitivity and precision

Copula modelling for multivariate statistical process control: a review

Horizontal inequity under a dual income tax system: principles and measurement

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