An Introduction to Copulas (Springer Series in Statistics) by Roger B. Nelsen

By Roger B. Nelsen

The examine of copulas and their function in data is a brand new yet vigorously growing to be box. during this publication the coed or practitioner of records and likelihood will locate discussions of the basic homes of copulas and a few in their fundamental purposes. The functions comprise the learn of dependence and measures of organization, and the development of households of bivariate distributions. This e-book is acceptable as a textual content or for self-study.

Show description

Read Online or Download An Introduction to Copulas (Springer Series in Statistics) PDF

Best computer simulation books

Digital systems design with VHDL and synthesis

Ok. C. Chang offers an built-in method of electronic layout ideas, procedures, and implementations to assist the reader layout more and more advanced platforms inside of shorter layout cycles. Chang introduces electronic layout strategies, VHDL coding, VHDL simulation, synthesis instructions, and methods jointly.

The LabVIEW Style Book (National Instruments Virtual Instrumentation Series)

&>   Drawing at the stories of a world-class LabVIEW improvement association, The LabVIEW sort e-book is the definitive advisor to most sensible practices in LabVIEW improvement. top LabVIEW improvement supervisor Peter A. Blume provides useful instructions or “rules” for optimizing each side of your purposes: ease of use, potency, clarity, simplicity, functionality, maintainability, and robustness.

Robot Cognition and Navigation: An Experiment with Mobile Robots (Cognitive Technologies)

This publication provides the concept that of cognition in a transparent, lucid and hugely complete sort. It offers an in-depth research of mathematical versions and algorithms, and demonstrates their software with actual existence experiments.

Innovating with Concept Mapping: 7th International Conference on Concept Mapping, CMC 2016, Tallinn, Estonia, September 5-9, 2016, Proceedings

This e-book constitutes the refereed lawsuits of the seventh overseas convention on thought Mapping, CMC 2016, held in Tallinn, Estonia, in September 2016. The 25 revised complete papers provided have been rigorously reviewed and chosen from a hundred thirty five submissions. The papers deal with matters similar to facilitation of studying; eliciting, taking pictures, archiving, and utilizing “expert” wisdom; making plans guide; evaluation of “deep” understandings; examine making plans; collaborative wisdom modeling; construction of “knowledge portfolios”; curriculum layout; eLearning, and administrative and strategic making plans and tracking.

Extra info for An Introduction to Copulas (Springer Series in Statistics)

Example text

5; see (Schweizer and Sklar 1983) for details. 4. 10 Multivariate Copulas 45 S1¥ S2 ¥L¥ Sn . Let x = ( x1 , x 2 ,L , x n ) and y = ( y1 , y 2 ,L , y n ) be any points in S1¥ S2 ¥L¥ Sn . Then n H ( x) - H ( y) £ Â H k ( xk ) - H k ( yk ) . k =1 We are now in a position to define n-dimensional subcopulas and copulas. 2. 5. An n-dimensional subcopula (or n-subcopula) is a function C ¢ with the following properties: 1. Dom C ¢ = S1¥ S2 ¥L¥ Sn , where each Sk is a subset of I containing 0 and 1; 2. C ¢ is grounded and n-increasing; 3.

3) We shall encounter this family again in Chapter 4. ■ Two other functions closely related to copulas—and survival copulas—are the dual of a copula and the co-copula (Schweizer and Sklar 1983). The dual of a copula C is the function C˜ defined by C˜ ( u , v ) = u + v - C ( u , v ) ; and the co-copula is the function C * defined by C * ( u , v ) = 1 - C (1 - u ,1 - v ) . Neither of these is a copula, but when C 34 2 Definitions and Basic Properties is the copula of a pair of random variables X and Y, the dual of the copula and the co-copula each express a probability of an event involving X and Y.

If F1 , F2 ,…, Fn are all continuous, C is unique. Otherwise, C is uniquely determined on Ran F1 ¥Ran F2 ¥L¥Ran Fn . 8) n W ( u) = max( u1 + u 2 ,+ L + u n - n + 1,0). 36). 5). 4. 12. If C ¢ is any n-subcopula, then for every u in Dom C ¢ , W n ( u) £ C ¢( u) £ M n ( u) . 13. For any n ≥ 3 and any u in In , there exists an ncopula C (which depends on u) such that C ( u) = W n ( u) . Proof (Sklar 1998). Let u = ( u1 , u 2 ,L , u n ) be a (fixed) point in In other than 0 = (0,0,…,0) or 1 = (1,1,…,1).

Download PDF sample

Rated 4.75 of 5 – based on 5 votes