## An Introduction to CopulasCopulas are functions that join multivariate distribution functions to their one-dimensional margins. 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. With 116 examples, 54 figures, and 167 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. The revised second edition includes new sections on extreme value copulas, tail dependence, and quasi-copulas. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of Proofs Without Words: Exercises in Visual Thinking and Proofs Without Words II: More Exercises in Visual Thinking, published by the Mathematical Association of America. |

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### Contents

V | 10 |

Definitions and Basic Properties | 14 |

22 Copulas | 17 |

23 Sklars Theorem | 24 |

VI | 28 |

VII | 30 |

VIII | 32 |

IX | 34 |

XXXI | 135 |

XXXII | 141 |

XXXIV | 146 |

XXXV | 150 |

XXXVI | 151 |

XXXVII | 155 |

XXXVIII | 156 |

XL | 158 |

X | 36 |

XI | 38 |

26 Survival Copulas | 39 |

XII | 40 |

XIII | 42 |

210 Multivariate Copulas | 49 |

XIV | 51 |

XVI | 52 |

XVII | 55 |

Exercises | 57 |

Methods of Constructing Copulas | 59 |

312 The Circular Uniform Distribution | 63 |

XVIII | 64 |

32 Geometric Methods | 67 |

Exercises | 72 |

XIX | 74 |

XX | 76 |

325 Copulas with Prescribed Horizontal or Vertical Sections | 84 |

XXI | 86 |

XXII | 89 |

326 Copulas with Prescribed Diagonal Sections | 92 |

Exercises | 94 |

33 Algebraic Methods | 97 |

XXIV | 99 |

XXV | 101 |

333 A Copula Transformation Method | 102 |

334 Extreme Value Copulas | 105 |

34 Copulas with Specified Properties | 109 |

XXVIII | 114 |

XXIX | 115 |

XXX | 132 |

XLI | 165 |

511 Kendalls tau | 167 |

XLII | 171 |

Exercises | 174 |

Exercises | 180 |

XLIII | 185 |

XLIV | 186 |

514 Other Concordance Measures | 189 |

XLV | 191 |

52 Dependence Properties | 195 |

523 Stochastic Monotonicity Corner Set Monotonicity and Likelihood Ratio Dependence | 204 |

XLVI | 207 |

XLVIII | 211 |

Exercises | 213 |

XLIX | 214 |

53 Other Measures of Association | 216 |

L | 217 |

LI | 219 |

Exercises | 222 |

55 Median Regression | 227 |

LII | 233 |

LIII | 236 |

LIV | 240 |

LV | 241 |

LVI | 244 |

LVII | 248 |

250 | |

References | 263 |

265 | |

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Comparison Methods for Stochastic Models and Risks Alfred Müller,Dietrich Stoyan No preview available - 2002 |