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An Introduction to Copulas
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TLDR
This book discusses the fundamental properties of copulas and some of their primary applications, which include the study of dependence and measures of association, and the construction of families of bivariate distributions.Abstract:
The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. This book is suitable as a text or for self-study.read more
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Journal ArticleDOI
Archimedean copula estimation using Bayesian splines smoothing techniques
TL;DR: A ratio approximation of the generator and of its first derivative using B-splines is proposed and the associated parameters estimated using Markov chains Monte Carlo methods, and the estimation is reasonably quick.
Journal ArticleDOI
A Versatile Probability Model of Photovoltaic Generation Using Pair Copula Construction
TL;DR: The proposed method can simplify the modeling procedure and provide a flexible and optimal probability model for the PV generation with complex dependence and is applied to the probabilistic load flow study of the IEEE 118-bus system.
Proceedings Article
Fairness-Aware Learning for Continuous Attributes and Treatments
TL;DR: This work exploits Witsenhausen’s characterization of the Rényi correlation coefficient to propose a differentiable implementation linked to f -divergences that allows fairness to be extented to variables such as mixed ethnic groups or financial status without thresholds effects.
Journal ArticleDOI
Sums of dependent nonnegative random variables with subexponential tails
Bangwon Ko,Qihe Tang +1 more
TL;DR: In this paper, the authors studied the asymptotic tail probabilities of sums of subexponential, nonnegative random variables, which are dependent according to certain general structures with tail independence.
Journal ArticleDOI
On two dependent individual risk models
TL;DR: In this article, the authors propose two constructions which allow dependence between the risks of an insurance portfolio in the individual risk model, and the impact on the cumulative distribution function of the aggregate claim amount and on the stop-loss premium is presented via numerical examples.