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Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality [Kõva köide]

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Edited by (Texas A&M University, College Station, USA)
  • Formaat: Hardback, 420 pages, kõrgus x laius: 234x156 mm, kaal: 721 g, 100 Illustrations, black and white
  • Ilmumisaeg: 27-Jul-2004
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1584884312
  • ISBN-13: 9781584884316
Teised raamatud teemal:
Skew-Elliptical Distributions and Their Applications: A Journey Beyond NormalitySuurem pilt
  • Formaat: Hardback, 420 pages, kõrgus x laius: 234x156 mm, kaal: 721 g, 100 Illustrations, black and white
  • Ilmumisaeg: 27-Jul-2004
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1584884312
  • ISBN-13: 9781584884316
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781584884316.html
Märksõnad:
In 1985, skew-normal distribution was articulated, which modifies the normal probability density function by a multiplicative skewing function, and since then the idea has been extended to elliptically contoured distributions, yielding various families of skew-elliptical distributions. Contributors from around the world review the current state of the art and describe new developments, reporting theoretical results and applications previous scattered throughout the literature. Among the 20 topics are elliptical models subject to hidden truncation or selective sampling, and skewed link models for categorical response data. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)

This book reviews the state-of-the-art advances in skew-elliptical distributions and provides many new developments in a single volume, collecting theoretical results and applications previously scattered throughout the literature. The main goal of this research area is to develop flexible parametric classes of distributions beyond the classical normal distribution. The book is divided into two parts. The first part discusses theory and inference for skew-elliptical distribution. The second part examines applications and case studies, including areas such as economics, finance, oceanography, climatology, environmetrics, engineering, image processing, astronomy, and biomedical science.
I Theory and Inference
1(172)
The Skew-Normal Distribution
3(22)
Alessandra Dalla Valle
Introduction
3(1)
The Univariate Skew-Normal Distribution
4(5)
Moments
7(1)
Cumulative Distribution Function
8(1)
Estimation and Inference
9(4)
Checking the Hypothesis of Skew-Normality
13(1)
The Multivariate Skew-Normal Distribution
14(5)
Genesis
15(1)
The Cumulative Distribution Function
16(1)
The Moment Generating Function
17(2)
Extensions of Properties Holding in the Scalar Case
19(1)
Quadratic Forms
20(2)
The Conditional Distribution
22(1)
Miscellanea
23(1)
Future Research Problems
24(1)
The Closed Skew-Normal Distribution
25(18)
Graciela Gonzalez-Farias
J. Armando Dominguez-Molina
Arjun K. Gupta
Introduction
25(1)
Basic Results on the Multivariate CSN Distribution
26(3)
Linear Transformations
29(4)
Joint Distribution of Independent CSN Random Vectors
33(2)
Sums of Independent CSN Random Vectors
35(2)
Examples of Sums of Skew-Normal Random Vectors
37(3)
Azzalini and Dalla Valle (1996)
37(1)
Arnold and Beaver (2002)
38(1)
Liseo and Loperfido (2003a)
39(1)
A Multivariate Extended Skew-Elliptical Distribution
40(1)
Concluding Remarks
41(2)
Skew-Elliptical Distributions
43(22)
Junfeng Liu
Dipak K. Dey
Introduction
43(1)
General Multivariate Skew-Elliptical Distributions
44(6)
The Branco and Dey Approach
45(1)
The Arnold and Beaver Approach
46(1)
The Wang-Boyer-Genton Approach
47(1)
The Dey and Liu Approach
48(1)
Linear Constraint and Linear Combination of Type-1 (LCLC1)
49(1)
Linear Constraint and Linear Combination of Type-2 (LCLC2)
49(1)
Examples of Skew-Elliptical Distributions
50(6)
Skew-Scale Mixture of Normal Distribution
50(1)
Skew-Finite Mixture of Normal
51(1)
Skew-Logistic Distribution
51(1)
Skew-Stable Distribution
51(1)
Skew-Exponential Power Distribution
52(1)
Skew-t Distribution
52(1)
Skew-Pearson Type II Distribution
53(1)
Different Types of Multivariate Skew-Normal Distributions
53(1)
Type A-SN(μ, Ω, α)
53(1)
Type B-SN(μ, Ω, D)
54(1)
The Liseo and Loperfido Class of SN
54(1)
The Dominguez-Molina-Gonzalez-Farias-Gupta Class of SN
54(1)
Skew-Elliptical Distribution SEk(μ, Ω, δ, g (k+1)
55(1)
Skew-Elliptical Distribution SEm(μ, Σ, D, g(m)
55(1)
Some Properties of Skew-Elliptical Distributions
56(6)
Moment Generating Functions
56(1)
Skew-Scale Mixture of Normal Distributions
56(2)
LCLC1
58(1)
LCLC2
58(1)
Marginal and Conditional Closure Property
58(1)
Distribution of Quadratic Forms
59(1)
LCLC1
59(1)
LCLC2
59(1)
Quadratic Forms from LCLC1/LCLC2
59(2)
Other Distributional Properties
61(1)
Properties of the Branco-Dey Skew-Elliptical Models
61(1)
Density Shape of Univariate Skew-Elliptical Distributions
62(1)
Concluding Remarks
62(3)
Generalized Skew-Normal Distributions
65(16)
Nicola M. R. Loperfido
Introduction
65(1)
Definition and Characterization
65(3)
Transformations and Moments
68(1)
Diagnostics
69(3)
Parametric Inference
72(2)
Australian Athletes Data
74(2)
Concluding Remarks
76(1)
Appendix: Proofs
77(4)
Skew-Symmetric and Generalized Skew-Elliptical Distributions
81(20)
Marc G. Genton
Introduction
81(1)
Skew-Symmetric Distributions
82(6)
Invariance
82(3)
Stochastic Representation and Simulations
85(1)
Skew-Symmetric Representation of Multivariate Distributions
86(1)
Example: Intensive Care Unit Data
86(2)
Generalized Skew-Elliptical Distributions
88(2)
Flexible Skew-Symmetric Distributions
90(10)
Flexibility and Multimodality
91(2)
Example: Australian Athletes Data
93(2)
Locally Efficient Semiparametric Estimators
95(5)
Concluding Remarks
100(1)
Elliptical Models Subject to Hidden Truncation or Selective Sampling
101(12)
Barry C. Arnold
Robert J. Beaver
Introduction
101(1)
Univariate Skew-Normal Models
101(2)
Estimation for the Skew-Normal Distribution
103(1)
Other Univariate Skewed Distributions
104(1)
Multivariate Skewed Distributions
105(2)
General Multivariate Skewed Distributions
107(2)
Hidden Truncation Paradigm
107(1)
Hidden Truncation, More General
107(1)
Additive Component Paradigm
108(1)
Additive Component, More General
108(1)
The Jones Construction
108(1)
Skew-Elliptical Distributions
109(3)
Discussion
112(1)
From Symmetric to Asymmetric Distributions: A Unified Approach
113(18)
Reinaldo B. Arellano-Valle
Guido E. del Pino
Introduction
113(2)
Signs, Absolute Values, and Skewed Distributions
115(2)
Latent Variables, Selection Models, Skewed Distributions
117(1)
Symmetry, Invariance, and Skewness
118(3)
Glossary and Basic Facts
118(1)
Three Groups of Transformations
119(1)
Conditional Representations
119(1)
Density or Probability Functions for the Maximal Invariant
120(1)
The SI Class of Sign Invariant Distributions
121(3)
Examples and Main Results
121(2)
Application to the Density Formula for a Skewed Distribution
123(1)
A Stochastic Representation Associated with the SI Class
124(2)
Moments of a Multivariate Skewed Distribution
125(1)
Distribution of the Square of a Skewed Random Variable
126(1)
Application to the Multivariate Skew-Normal Distribution
126(2)
A Canonical Form for Skew-Elliptical Distributions
128(3)
Skewed Link Models for Categorical Response Data
131(22)
Ming-Hui Chen
Introduction
131(1)
Preliminaries
132(2)
Importance of Links in Fitting Categorical Response Data
134(3)
Relationship between Regression Coefficients under Different Links
134(1)
Prediction under Different Links
135(2)
General Skewed Link Models
137(6)
Independent Binary and/or Ordinal Regression Models
137(3)
Correlated Binary and/or Ordinal Regression Models
140(2)
Discrete Choice Models
142(1)
Bayesian Inference
143(1)
Bayesian Model Assessment
144(4)
Weighted L Measure
144(3)
Conditional Predictive Ordinate
147(1)
Deviance Information Criterion
148(1)
Bayesian Model Diagnostics and Outlier Detection
148(3)
Bayesian Latent Residuals
149(1)
Bayesian CPO-Based Residuals
149(1)
Observationwise Weighted L Measure
150(1)
Concluding Remarks
151(2)
Skew-Elliptical Distributions in Bayesian Inference
153(20)
Brunero Liseo
Introduction
153(1)
Skewed Prior Distributions for Location Parameters
154(4)
Hierarchical Models with Linear Constraints
154(2)
Efficiency of Linear Bayes Rules with Skewed Priors
156(1)
Heavy Tail Priors
157(1)
Skew-Elliptical Likelihood
158(5)
Inferential Problems
159(1)
Regression Models with SE Errors
160(2)
Some Applications
162(1)
Objective Bayesian Analysis of the Skew-Normal Model
163(6)
The Scalar Case
164(2)
Some Multivariate Results
166(3)
Appendix
169(4)
II Applications and Case Studies
173(186)
Bayesian Multivariate Skewed Regression Modeling with an Application to Firm Size
175(16)
Jose T. A. S. Ferreira
Mark F. J. Steel
Introduction
175(1)
Multivariate Skewed Distributions
176(3)
FS Skewed Distributions
177(1)
SDB Skewed Distributions
178(1)
Regression Models
179(2)
Prior Distributions
179(1)
Numerical Implementation
180(1)
Application to Firm Size
181(8)
Distribution of Firm Size
183(3)
Analysis of Firm Growth
186(3)
Discussion
189(2)
Capital Asset Pricing for UK Stocks under the Multivariate Skew-Normal Distribution
191(14)
Chris Adcock
Introduction
191(3)
The Multivariate Skew-Normal Model
194(2)
The Market Model
196(2)
Estimation Methodology and Data
198(1)
Empirical Study
199(5)
Summary and Conclusions
204(1)
A Skew-in-Mean GARCH Model
205(18)
Giovanni De Luca
Nicola M. R. Loperfido
Introduction
205(2)
Assumptions
207(1)
News
208(2)
Returns
210(1)
Data
211(2)
Estimation
213(2)
Conclusions
215(1)
Appendix
216(7)
Skew-Normality in Stochastic Frontier Analysis
223(20)
J. Armando Dominguez-Molina
Graciela Gonzalez-Farias
Rogelio Ramos-Quiroga
Introduction
223(2)
Estimation
225(5)
Model Assumptions
226(1)
Model I: Homoscedastic and Uncorrelated Errors
227(1)
Model II: Heteroscedastic and Uncorrelated Errors
227(1)
Model III: Correlated Errors
227(1)
Likelihood
228(1)
Estimation of Inefficiencies/Efficiencies
229(1)
A Correlated Structure for the Compound Error
230(4)
Simulated Example with Correlated Compound Errors
231(3)
SFA with Skew-Elliptical Components
234(1)
Conclusions
235(1)
Appendix
236(7)
Distributional Properties of Multivariate Compound Errors
236(2)
Expectation of the Truncated Multivariate Normal Distribution
238(1)
Efficiencies for Individual Errors of Model III
239(4)
Coastal Flooding and the Multivariate Skew-t Distribution
243(16)
Keith R. Thompson
Yingshuo Shen
Introduction
243(1)
A Seasonally Varying Skew-t Distribution
244(3)
Observations of Coastal Sea Level
247(3)
Fitting the Skew-t Distribution
250(3)
Applications of the Skew-t Distribution
253(5)
Quality Control of Sea Level Observations
253(1)
Detecting Secular Changes in the Sea Level Distribution
254(1)
Estimating Flooding Risk
255(3)
Discussion
258(1)
Time Series Analysis with a Skewed Kalman Filter
259(20)
Philippe Naveau
Marc G. Genton
Caspar Ammann
Introduction
259(1)
The Classical Kalman Filter
260(2)
State-Space Model
260(1)
The Kalman Filter Procedure in the Gaussian Case
261(1)
A Skewed Kalman Filter
262(6)
The Closed Skew-Normal Distribution
262(1)
Extension of the Linear Gaussian State-Space Model
263(2)
The Steps of our Skewed Kalman Filter
265(3)
Applications to Paleoclimate Time Series
268(6)
Multi-Process Linear Models
269(1)
The Smoothing Spline Model for Trends
269(1)
The Skewed Component
270(3)
The State-Space Model
273(1)
Simulations and Results
273(1)
Conclusions
274(1)
Appendix
275(4)
Spatial Prediction of Rainfall Using Skew-Normal Processes
279(12)
Hyoung-Moon Kim
Eunho Ha
Bani K. Mallick
Introduction
279(1)
Data and Model
280(4)
Automatic Weather Stations and Their Sensors
280(1)
Model Description
280(2)
Bayesian Analysis
282(2)
Data Analyses
284(4)
Discussion
288(3)
Shape Representation with Flexible Skew-Symmetric Distributions
291(18)
Sajjad H. Baloch
Hamid Krim
Marc G. Genton
Introduction
291(1)
Problem Statement
292(2)
Shape Analysis
294(8)
Posterior Learning
296(3)
Selection of a Distribution for the Angle
299(1)
Overall Shape Distribution
300(1)
Performance Assessment of the Learning Process
301(1)
Experimental Results
302(5)
Case Study 1
303(1)
Case Study 2
304(1)
Case Study 3
304(1)
Case Study 4
305(1)
Case Study 5
305(1)
Sampling from Models
306(1)
Conclusions
307(1)
Appendix
308(1)
An Astronomical Distance Determination Method Using Regression with Skew-Normal Errors
309(12)
Laurent Eyer
Marc G. Genton
Introduction
309(1)
The Trigonometric Parallax
310(2)
Astrometric Satellites
311(1)
Some Statistical Aspects
311(1)
Parallax Is a Positive Quantity
311(1)
Parent Distribution
312(1)
Formation of Samples
312(1)
Famous Standard Candles: the Cepheids
312(2)
Calibration of the Period-Luminosity Relation
314(7)
Regression with Skew-Normal Errors
315(1)
Discussion
316(1)
Fixed Slope
316(1)
Free Slope
317(4)
On a Bayesian Multivariate Survival Model with a Skewed Frailty
321(18)
Sujit K. Sahu
Dipak K. Dey
Introduction
321(2)
Frailty Models
323(3)
Frailty Distributions
323(2)
Comparison of Frailty Distributions
325(1)
Baseline Hazard Function
326(1)
Model Specification
327(3)
Likelihood Specification
327(1)
Prior Specification
328(1)
Hyper-Parameter Values and Prior Sensitivity
329(1)
Reversible Jump Steps
330(2)
Examples
332(4)
Kidney Infection Data Example
332(2)
Litters Example
334(2)
Conclusion
336(3)
Linear Mixed Effects Models with Flexible Generalized Skew-Elliptical Random Effects
339(20)
Yanyuan Ma
Marc G. Genton
Marie Davidian
Introduction
339(1)
FGSE Distributions and the Linear Mixed Effects Model
340(3)
Implementation and Inference
343(7)
Maximum Likelihood via the EM Algorithm
343(3)
Bayesian Inference via Markov Chain Monte Carlo Simulation
346(4)
Simulation Results
350(6)
Application to Cholesterol Data
356(2)
Discussion
358(1)
References 359(18)
Index 377
Marc G. Genton