@article{Solow1988,
abstract = {Two statistical tests for correlation between a circular variate and a linear variate are presented. The tests are applied to a small data set concerning Freon-12 concentration and wind direction in Woods Hole, Massachusetts during the summer of 1987. A significant correlation is found. Further analysis suggests that this directional effect is related to onshore Freon-12 release.},
author = {Solow, Andrew R and Bullister, John L and Nevison, Cynthia},
doi = {10.1007/BF00395081},
file = {:C$\backslash$:/Users/Flo/Documents/ETH/pop{\_}eco/copula/literature/correlation/Solow 1988.pdf:pdf},
issn = {1573-2959},
journal = {Environmental Monitoring and Assessment},
number = {3},
pages = {219--228},
title = {{An application of circular-linear correlation analysis to the relationship between Freon concentration and wind direction in Woods Hole, Massachusetts}},
url = {https://doi.org/10.1007/BF00395081/},
volume = {10},
year = {1988}
}
@article{Mardia1976,
abstract = {[We propose some correlation coefficients when one variable is linear and another is circular. These are motivated by a study which investigates the relationship between geographic latitude and simian natality.]},
author = {Mardia, K V},
doi = {10.2307/2335637},
file = {:C$\backslash$:/Users/Flo/Documents/ETH/pop{\_}eco/copula/literature/correlation/Mardia 1976.pdf:pdf},
issn = {00063444},
journal = {Biometrika},
number = {2},
pages = {403--405},
publisher = {[Oxford University Press, Biometrika Trust]},
title = {{Linear-Circular Correlation Coefficients and Rhythmometry}},
volume = {63},
year = {1976}
}
@article{Tu2015,
abstract = {A simulation study of the parametric and nonparametric Linear-Circular Correlation Coefficient was carried out to evaluate the mathematical distribution the statistics followed. A further study was conducted to investigate the effect of ties on the nonparametric correlation coefficient. Lastly, a com-parison of power between the parametric and nonparametric Linear-Circular Correlation coefficient was conducted with varying sample sizes, means, and distributions.},
author = {Tu, Robin},
file = {:C$\backslash$:/Users/Flo/Documents/ETH/pop{\_}eco/copula/literature/correlation/Tu 2015.pdf:pdf},
journal = {California Polytechnic State University, San Luis Obispo},
pages = {1--24},
title = {{A Study of the Parametric and Nonparametric Linear-Circular Correlation Coefficient}},
url = {https://digitalcommons.calpoly.edu/statsp/51/},
year = {2015}
}
@article{Nelsen1997,
abstract = {In this paper we present a method for construction families of bivariate copulas with cubic cross-sections. We study dependence properties, measures of association, and concepts of symmetry for these copulas. Examples of both symmetric and asymmetric copulas with cubic sections are presented which extend some well known families of bivariate copulas (such as the iterated Farlie-Gumbel-Morgenstern, Kimeldorf and Sampson, Lin, and Sarmanov families of copulas) and which provide second-order approximations to the Frank and Plackett families of copulas.},
author = {Nelsen, R. B. and Quesada-Molina, J. J. and Rodr{\'{i}}guez-Lallena, J. A.},
doi = {10.1080/10485259708832700},
file = {:C\:/Users/Flo/Documents/ETH/pop_eco/copula/literature/types of copulas/Nelsen 1997.pdf:pdf},
issn = {10485252},
journal = {Journal of Nonparametric Statistics},
keywords = {Concepts of dependence,Copulas,Families of bivariate copulas,Measures of association,Radial symmetry},
number = {3},
pages = {205--220},
title = {{Bivariate copulas with cubic sections}},
volume = {7},
year = {1997}
}
@article{Quesada-Molina1995,
abstract = {In this paper we present a method for constructing bivariate copulas with quadratic sections. These copulas are derived from simple univariate real-valued functions on the interval [0,1]. As a consequence, various positive dependence properties (such as quadrant dependence and total positivity), measures of association (such as Spearman's rho and Kendall's tau), stochastic orderings, and various notions of symmetry are shown to be equivalent to certain simple properties of the above-mentioned univariate functions. Several examples, some of which can be viewed as generalizations of the Farlie-Gumbel-Morgenstern family, are presented to illustrate the facility with which these copulas can be constructed. {\textcopyright} 1995 OPA (Overseas Publishers Association).},
author = {Quesada-Molina, J. J. and Rodr{\'{i}}guez-Lallena, J. A.},
doi = {10.1080/10485259508832652},
file = {:C\:/Users/Flo/Documents/ETH/pop_eco/copula/literature/types of copulas/Bivariate copulas with quadratic sections.pdf:pdf},
issn = {10290311},
journal = {Journal of Nonparametric Statistics},
keywords = {Concepts of dependence,Copulas,Families of bivariate copulas,Measures of dependence,Radial symmetry,Stochastic orderings},
number = {4},
pages = {323--337},
title = {{Bivariate copulas with quadratic sections}},
volume = {5},
year = {1995}
}
@book{Nelsen2006,
address = {New York, NY},
author = {Nelsen, Roger B.},
doi = {10.1007/978-1-4757-3076-0},
file = {:C\:/Users/Flo/Documents/ETH/pop_eco/copula/literature/review_n_books/2006_Nelsen_Book_AnIntroductionToCopulas.pdf:pdf},
isbn = {978-0-387-98623-4},
issn = {01727397},
keywords = {Springer series in statistics},
pages = {1--656},
pmid = {15772297},
publisher = {Springer New York},
series = {Lecture Notes in Statistics},
title = {{An Introduction to Copulas}},
url = {https://link.springer.com/book/10.1007/978-1-4757-3076-0},
volume = {139},
year = {2006}
}
@book{Durante2015,
author = {Durante, Fabrizio and Sempi, Carlo},
doi = {10.1201/b18674},
file = {:C\:/Users/Flo/Documents/ETH/pop_eco/copula/literature/review_n_books/book_p[rinciples_of_copula_tehory.pdf:pdf},
isbn = {9780429066399},
month = {jul},
publisher = {Chapman and Hall/CRC},
title = {{Principles of Copula Theory}},
url = {https://www.taylorfrancis.com/books/9781439884447/},
year = {2015}
}
@article{MariusHofert2011,
author = {{Marius Hofert} and {Martin M{\"{a}}chler}},
journal = {Journal of Statistical Software},
number = {9},
pages = {1--20},
title = {{Nested Archimedean Copulas Meet {R}: The {nacopula} Package}},
url = {https://www.jstatsoft.org/v39/i09/},
volume = {39},
year = {2011}
}
@article{JunYan2007,
author = {{Jun Yan}},
journal = {Journal of Statistical Software},
number = {4},
pages = {1--21},
title = {{Enjoy the Joy of Copulas: With a Package {copula}}},
url = {https://www.jstatsoft.org/v21/i04/},
volume = {21},
year = {2007}
}
@book{Hofert2018,
author = {Hofert, Marius and Kojadinovic, Ivan and Maechler, Martin and Yan, Jun},
file = {:C\:/Users/Flo/Documents/ETH/pop_eco/copula/literature/review_n_books/2018_Book_ElementsOfCopulaModelingWithR.pdf:pdf},
isbn = {978-3-319-89634-2},
publisher = {Springer Use R! Series},
title = {{Elements of Copula Modeling with R}},
url = {https://www.springer.com/de/book/9783319896342/},
year = {2018}
}
@article{Nadarajah2017,
author = {Nadarajah, Saralees and Zhang, Yuanyuan},
doi = {10.1371/journal.pone.0188512},
journal = {PLOS ONE},
pages = {e0188512},
title = {{Wrapped: An R package for circular data}},
volume = {12},
year = {2017}
}
@manual{Hofert2020,
annote = {R package version 1.0-1},
author = {Hofert, Marius and Kojadinovic, Ivan and Maechler, Martin and Yan, Jun},
title = {{copula: Multivariate Dependence with Copulas}},
url = {https://cran.r-project.org/package=copula/},
year = {2020}
}
@article{Durante2009,
abstract = {We present a method for constructing bivariate copulas by changing the values that a given copula assumes on some subrectangles of the unit square. Some applications of this method are discussed, especially in relation to the construction of copulas with different tail dependencies.},
author = {Durante, Fabrizio and Saminger-Platz, Susanne and Sarkoci, Peter},
doi = {10.1080/03610920802571203},
file = {:C\:/Users/Flo/Documents/ETH/pop_eco/copula/literature/circ-lin_copulas/Durante 2009.pdf:pdf},
issn = {03610926},
journal = {Communications in Statistics - Theory and Methods},
keywords = {Copula,Exchangeability,Sections of copulas,Tail dependence},
number = {15},
pages = {2515--2527},
title = {{Rectangular patchwork for bivariate copulas and tail dependence}},
volume = {38},
year = {2009}
}
@article{Johnson1978,
abstract = {The second edition of this book widens the scope of the methods and applications of Applied Multivariate Statistical Analysis. We have introduced more up to date data sets in our examples. These give the text a higher degree of timeliness and add an even more applied flavour. Since multivariate statistical methods are heavily used in quantitative finance and risk management we have put more weight on the presentation of distributions and their densities. We discuss in detail different families of heavy tailed distributions (Laplace, Generalized Hy- perbolic). We also devoted a section on copulae, a new concept of dependency used in the financial risk management and credit scoring. In the chapter on computer intensive meth- ods we have added support vector machines, a new classification technique from statistical learning theory. We apply this method to bankruptcy and rating analysis of firms. The very important CART (Classification and Regression Tree) technique is also now inserted into this chapter. We give an application to rating of companies. The probably most important step towards readability and user friendliness of this book is that we have translated all Quantlets into the R and Matlab language. The algorithms can be downloaded from the authors' web sites. In the preparation of this 2nd edition, we received helpful output from Anton Andriyashin, Ying Chen, Song Song and Uwe Ziegenhagen. We would like to thank them.},
author = {Johnson, Richard A. and Wehrly, Thomas E.},
doi = {10.2307/1270921},
file = {:C\:/Users/Flo/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Johnson, Wehrly - 1978 - Some Angular-Linear Distributions and Related Regression Models.pdf:pdf},
issn = {00401706},
journal = {Journal of the American Statistical Association ISSN:},
keywords = {1977,and wehrly,angular-linear distribution,butions appears in johnson,directional data,entropy,for angular-linear distri-,gression,re-,taining measures of dependence,trigonometric regression},
number = {363},
pages = {602--606},
title = {{Some Angular-Linear Distributions and Related Regression Models}},
volume = {73},
year = {1978}
}
@article{Hornik2014,
author = {Hornik, Kurt and Gr{\"{u}}n, Bettina},
doi = {10.18637/jss.v058.i10},
journal = {Journal of Statistical Software},
title = {{movMF : An R Package for Fitting Mixtures of von Mises-Fisher Distributions}},
volume = {58},
year = {2014}
}
@article {Hodelappl,
	author = {Hodel, Florian H. and Fieberg, John R.},
	title = {Circular-Linear Copulae for Animal Movement Data},
	elocation-id = {2021.07.14.452404},
	year = {2022},
	doi = {10.1111/2041-210X.13821},
	journal = {Methods in Ecology and Evolution}
}
@article {Hodelmethod,
	author = {Hodel, Florian H. and Fieberg, John R.},
	title = {Cylcop: An R Package for Circular-Linear Copulae with Angular Symmetry},
	year = {2021},
	doi = {10.1101/2021.07.14.452253},
	publisher = {Cold Spring Harbor Laboratory},
	URL = {https://www.biorxiv.org/content/10.1101/2021.07.14.452253v3/},
	journal = {bioRxiv}
}
@article{Jian2011,
title = {Mutual Information Is Copula Entropy},
journal = {Tsinghua Science and Technology},
volume = {16},
number = {1},
pages = {51-54},
year = {2011},
issn = {1007-0214},
doi = {https://doi.org/10.1016/S1007-0214(11)70008-6},
url = {https://www.sciencedirect.com/science/article/pii/S1007021411700086/},
author = {Jian Ma and Zengqi Sun},
keywords = {copula entropy, mutual information, estimation, empirical copula},
abstract = {Mutual information (MI) is a basic concept in information theory. Therefore, estimates of the MI are fundamentally important in most information theory applications. This paper provides a new way of understanding and estimating the MI using the copula function. First, the entropy of the copula, named the copula entropy, is defined as a measure of the dependence uncertainty represented by the copula function and then the MI is shown to be equivalent to the negative copula entropy. With this equivalence, the MI can be estimated by first estimating the empirical copula and then estimating the entropy of the empirical copula. Thus, the MI estimate is an estimation of the entropy, which reduces the complexity and computational requirements. Tests show that the method is more effective than the traditional method.}
}
@article{Calsaverini2009,
author = {Calsaverini, R S and Vicente, R and Systems, Complex and Artes, Escola De},
doi = {10.1209/0295-5075/88/68003},
file = {:C\:/Users/Flo/Documents/ETH/pop_eco/copula/literature/Mutual information/Calsaverini 2009.pdf:pdf},
journal = {Europhysics Letters},
number = {6},
pages = {1--6},
title = {{An information-theoretic approach to statistical dependence: Copula information}},
volume = {88},
year = {2009},
url = {https://iopscience.iop.org/article/10.1209/0295-5075/88/68003/}
}
@article{Genest2008,
author = {Christian Genest and Bruno R{\'e}millard},
title = {{Validity of the parametric bootstrap for goodness-of-fit testing in semiparametric models}},
volume = {44},
journal = {Annales de l'Institut Henri Poincaré, Probabilités et Statistiques},
number = {6},
publisher = {Institut Henri Poincaré},
pages = {1096 -- 1127},
keywords = {copula, Goodness-of-fit test, Monte Carlo simulation, Parametric bootstrap, P-values, Semiparametric estimation},
year = {2008},
doi = {10.1214/07-AIHP148},
URL = {https://doi.org/10.1214/07-AIHP148}
}


