Principles of copula theory. (2014)

• Record Type: Book
• Further Information: Note: Fabrizio Durante, Carlo Sempi.
• Authors: Durante, Fabrizio; Sempi, Carlo
• Contents: Copulas: Basic Definitions and Properties; Notations; Preliminaries on random variables and distribution functions; Definition and first examples; Characterization in terms of properties of d.f.s; Continuity and absolutely continuity; The derivatives of a copula; The space of copulas; Graphical representations Copulas and Stochastic Dependence; Construction of multivariate stochastic models via copulas; Sklar’s theorem; Proofs of Sklar’s theorem; Copulas and risk-invariant property; Characterization of basic dependence structures via copulas; Copulas and order statistics Copulas and Measures; Copulas and d -fold stochastic measures; Absolutely continuous and singular copulas; Copulas with fractal support; Copulas, conditional expectation, and Markov kernel; Copulas and measure-preserving transformations; Shuffles of a copula; Sparse copulas; Ordinal sums; The Kendall distribution function Copulas and Approximation; Uniform approximations of copulas; Application to weak convergence of multivariate d.f.s; Markov kernel representation and related distances; Copulas and Markov operators; Convergence in the sense of Markov operators The Markov Product of Copulas; The Markov product; Invertible and extremal elements in C 2 ; Idempotent copulas, Markov operators, and conditional expectations The Markov product and Markov processes; A generalization of the Markov product A Compendium of Families of Copulas; What is a family of copulas?; Fréchet copulas; EFGM copulas; Marshall-Olkin copulas; Archimedean copulas; Extreme-value copulas; Elliptical copulas; Invariant copulas under truncation Generalizations of Copulas: Quasi-Copulas; Definition and first properties; Characterizations of quasi-copulas; The space of quasi-copulas and its lattice structure; Mass distribution associated with a quasi-copula Generalizations of Copulas: Semi-Copulas; Definition and basic properties; Bivariate semi-copulas, triangular norms, and fuzzy logic; Relationships among capacities and semi-copulas; Transforms of semi-copulas; Semi-copulas and level curves; Multivariate aging notions of NBU and IFR Bibliography Index
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2014
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 519.535; Copulas (Mathematical statistics); Multivariate analysis
• Languages: English
• ISBNs: 9781439884447
• Related ISBNs: 9781439884423
• Notes: Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.