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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
On Default Correlation: A Copula Function Approach
TL;DR: In this paper, the authors introduce a random variable called "time-until-default" to denote the survival time of each defaultable entity or financial instrument, and define the default correlation between two credit risks as the correlation coefficient between their survival times.
OtherDOI
Continuous Multivariate Distributions
TL;DR: In this article, the authors present a concise review of developments on various continuous multivariate distributions and present some basic definitions and notations, and present several important continuous multi-dimensional distributions and their significant properties and characteristics.
Book
Introductory Lectures on Fluctuations of Lévy Processes with Applications
TL;DR: In this paper, the authors present decompositions of the paths of Levy processes in terms of their local maxima and an understanding of their short-and long-term behaviour.
Journal ArticleDOI
Sparse and Compositionally Robust Inference of Microbial Ecological Networks
Zachary D. Kurtz,Christian L. Müller,Emily R. Miraldi,Dan R. Littman,Martin J. Blaser,Richard Bonneau +5 more
TL;DR: SParse InversE Covariance Estimation for Ecological Association Inference is presented, a statistical method for the inference of microbial ecological networks from amplicon sequencing datasets that outperforms state-of-the-art methods to recover edges and network properties on synthetic data under a variety of scenarios.
Journal ArticleDOI
Goodness-of-fit tests for copulas: A review and a power study
TL;DR: In this paper, the authors present a critical review of the blanket test procedures and suggest new ones for goodness-of-fit testing of copula models, and describe and interpret the results of a large Monte Carlo experiment designed to assess the effect of the sample size and the strength of dependence on the level and power of blanket tests for various combinations of Copula models under the null hypothesis and the alternative.