This book introduces the main theoretical findings related to copulas and shows how statistical modeling of multivariate continuous distributions using copulas can be carried out in the R statistical environment with the package copula (among others). Copulas are multivariate distribution functions with standard uniform univariate margins. They are increasingly applied to modeling dependence among random variables in fields such as risk management, actuarial science, insurance, finance, engineering, hydrology, climatology, and meteorology, to name a few. In the spirit of the Use R! series, each chapter combines key theoretical definitions or results with illustrations in R. Aimed at statisticians, actuaries, risk managers, engineers and environmental scientists wanting to learn about the theory and practice of copula modeling using R without an overwhelming amount of mathematics, the book can also be used for teaching a course on copula modeling.
This book introduces the main theoretical findings related to copulas and shows how statistical modeling of multivariate continuous distributions using copulas can be carried out in the R statistical environment with the package copula ...
This book provides an interdisciplinary approach that creates advanced probabilistic models for engineering fields, ranging from conventional fields of mechanical engineering and civil engineering, to electronics, electrical, earth sciences ...
(b) The proof is the same but with more complex notation and more functions of the form of wi. L Remark 8.2 In a careful look at the proof, for part (a), the condition on the w functions can be weakened from c. to c's, where |S| is the ...
3.2 3.3 3.4 3.5 3.6 Show that a version of the Marshall-Olkin bivariate distribution with Pareto margins (see Example 2.14) has joint survival functions given by H(x,y)=(1+x)" (1+y)*[max(1+x, 1+y)]”, for x,y 20, where 6, 6, ...
ÁÀ n j1⁄41n w ij dðÀ Þ zi ̄z zj À ̄z Á . IdðÞ1⁄4W dðÞ P n i1⁄41 P P i1⁄41n z i À À ̄z À Á2 ð5.4Þ Notice how similar Moran's I and Pearson correlation coefficients are: in essence Moran's I(d) is a Pearson's coefficient computed for one ...
In the discussion of Fisher information in Sect.5.10, θ was assumed to be one-dimensional. ... second-order partial derivatives of − log{L(θ)}.1 In other words, the i, jth entry of the Fisher information matrix is Iij (θ) = −E ...
The book explains the pair-copula construction principles underlying these statistical models and discusses how to perform model selection and inference.
... 94, 134, 139, 143, 185,439, 512, 514,571, 572, 574, 577, 579,581, 589, 590, 624, 629 Tukey, J.W., 2, 4, 22, 105, 106, 110, 111, 112, 112, 113, 113, 114, 114, 134 Tversky, A., 2 Tyrer, P.J., 159, 185 U Ury, H.K., 304, 305 V Vanbelle, ...
Copula Modeling explores the copula approach for econometrics modeling of joint parametric distributions.
The credit crisis and ongoing European sovereign debt crisis have shown the importance of the proper assessment and management of counterparty risk. This book focuses on the interaction and possible overlap between DVA and FVA terms.