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

By Roger B. Nelsen

The learn of copulas and their function in facts is a brand new yet vigorously turning out to be box. during this publication the scholar or practitioner of facts and likelihood will locate discussions of the basic houses of copulas and a few in their fundamental purposes. The purposes comprise the research of dependence and measures of organization, and the development of households of bivariate distributions. This ebook 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

Autonomy Oriented Computing From Problem Solving to Complex Systems Modeling

Autonomy orientated Computing is a accomplished reference for scientists, engineers, and different pros desirous about this promising improvement in computing device technological know-how. it will possibly even be used as a textual content in graduate/undergraduate courses in a large diversity of computer-related disciplines, together with Robotics and Automation, Amorphous Computing, photograph Processing, Programming Paradigms, Computational Biology, and so forth.

Model Based Parameter Estimation: Theory and Applications

This really appropriate collection of articles combines mathematical and numerical the right way to practice parameter estimation and optimal experimental layout in a number of contexts. those contain fields as different as biology, medication, chemistry, environmental physics, snapshot processing and desktop imaginative and prescient. the fabric selected was once offered at a multidisciplinary workshop on parameter estimation held in 2009 in Heidelberg.

Reviews in Computational Chemistry, Volume 20

THIS quantity, LIKE these sooner than IT, gains CHAPTERS through specialists IN numerous FIELDS OF COMPUTATIONAL CHEMISTRY. themes lined IN quantity 20 comprise VALENCE thought, ITS heritage, basics, AND purposes; MODELING OF SPIN-FORBIDDEN REACTIONS; CALCULATION OF THE digital SPECTRA of enormous MOLECULES; SIMULATING CHEMICAL WAVES AND styles; FUZZY SOFT-COMPUTING equipment AND THEIR purposes IN CHEMISTRY; AND improvement OF COMPUTATIONAL versions FOR ENZYMES, TRANSPORTERS, CHANNELS, AND RECEPTORS suitable TO ADME/TOX.

Applications of Soft Computing in Time Series Forecasting: Simulation and Modeling Techniques

This publication stories on an in-depth research of fuzzy time sequence (FTS) modeling. It stories and summarizes prior examine paintings in FTS modeling and in addition presents a quick creation to different soft-computing suggestions, reminiscent of synthetic neural networks (ANNs), tough units (RS) and evolutionary computing (EC), concentrating on how those concepts could be built-in into varied stages of the FTS modeling procedure.

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

Example text

The random variables max(X,Y) and min(X,Y) are the order statistics for X and Y. Prove that the distribution functions of the order statistics are given by P[max( X ,Y ) £ t] = C ( F ( t),G ( t)) and P[min( X ,Y ) £ t] = F ( t) + G ( t) – C ( F ( t),G ( t)) , so that when F = G, P[max( X ,Y ) £ t ] = d C ( F ( t)) and P[min( X ,Y ) £ t] = 2 F ( t) – d C ( F ( t)) . (b) Show that bounds on the distribution functions of the order statistics are given by max( F ( t) + G ( t) - 1,0) £ P[max( X ,Y ) £ t] £ min( F ( t),G ( t)) and max( F ( t),G ( t)) £ P[min( X ,Y ) £ t] £ min( F ( t) + G ( t),1) .

Let (a,b) be any point in R 2 , and consider the following distribution function H: Ï0, x < a or y < b, H ( x, y) = Ì Ó1, x ≥ a and y ≥ b. The margins of H are the unit step functions e a and e b . 4 yields the subcopula C ¢ with domain {0,1}¥{0,1} such that C ¢ (0,0) = C ¢ (0,1) = C ¢ (1,0) = 0 and C ¢ (1,1) = 1. , C(u,v) = uv. Notice however, that every copula agrees with C ¢ on its domain, and thus is an extension of this C ¢ . ■ We are now ready to prove Sklar’s theorem, which we restate here for convenience.

Consider the set of points v where each v k is 0, 1, or tk = = ( v1 , v 2 ,L , v n ) min{( n - 1) u k ( u1 + u 2 + L + u n ) ,1} . Define an n-place function C ¢ on these points by C ¢( v ) = W n ( v ) . 5 and hence is an nsubcopula. 2). Then for each x in the n-box [0,t], t = ( t1 , t2 ,L , tn ) (which includes u), C ( x ) = W n ( x ) = 0. 2. Suppose n – 1 < u1 + u 2 + L + u n < n, and consider the set of points v = ( v1 , v 2 ,L , v n ) where now each v k is 0, 1, or sk = 1 – (1 - u k ) [ n - ( u i + u 2 + L + u n )] .

Download PDF sample

Rated 4.84 of 5 – based on 25 votes