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Majorization and the Lorenz Order with Applications in Applied Mathematics and Economics 2018 ed. [Kõva köide]

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  • Formaat: Hardback, 272 pages, kõrgus x laius: 235x155 mm, kaal: 606 g, 11 Illustrations, color; 7 Illustrations, black and white; XVII, 272 p. 18 illus., 11 illus. in color., 1 Hardback
  • Sari: Statistics for Social and Behavioral Sciences
  • Ilmumisaeg: 11-Aug-2018
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319937723
  • ISBN-13: 9783319937724
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Majorization and the Lorenz Order with Applications in Applied Mathematics and Economics 2018 ed.Suurem pilt
  • Formaat: Hardback, 272 pages, kõrgus x laius: 235x155 mm, kaal: 606 g, 11 Illustrations, color; 7 Illustrations, black and white; XVII, 272 p. 18 illus., 11 illus. in color., 1 Hardback
  • Sari: Statistics for Social and Behavioral Sciences
  • Ilmumisaeg: 11-Aug-2018
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319937723
  • ISBN-13: 9783319937724
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319937724.html
This book was written to serve as a graduate-level textbook for special topics classes in mathematics, statistics, and economics, to introduce these topics to other researchers, and for use in short courses. It is an introduction to the theory of majorization and related notions, and contains detailed material on economic applications of majorization and the Lorenz order, investigating the theoretical aspects of these two interrelated orderings. 

Revising and expanding on an earlier monograph, Majorization and the Lorenz Order: A Brief Introduction, the authors provide a straightforward development and explanation of majorization concepts, addressing historical development of the topics, and providing up-to-date coverage of families of Lorenz curves. The exposition of multivariate Lorenz orderings sets it apart from existing treatments of these topics.

Mathematicians, theoretical statisticians, economists, and other social scientists who already recognize the utility of the Lorenz order in income inequality contexts and arenas will find the book useful for its sound development of relevant concepts rigorously linked to both the majorization literature and the even more extensive body of research on economic applications. 

Barry C. Arnold, PhD, is Distinguished Professor in the Statistics Department at the University of California, Riverside. He is a Fellow of the American Statistical Society, the American Association for the Advancement of Science, and the Institute of Mathematical Statistics, and is an elected member of the International Statistical Institute. He is the author of more than two hundred publications and eight books.

José María Sarabia, PhD, is Professor of Statistics and Quantitative Methods in Business and Economics in the Department of Economics at the University of Cantabria, Spain. He is author of more than one hundred and fifty publications and ten books and is an associate editor of several journals including TEST, Communications in Statistics, and Journal of Statistical Distributions and Applications. 
1 Introduction
1(8)
1.1 Early Work About Majorization
1(4)
1.2 The Definition of Majorization
5(4)
2 Majorization in R+n
9(14)
2.1 Basic Result
9(4)
2.2 Schur Convex Functions and Majorization
13(8)
2.3 Exercises
21(2)
3 The Lorenz Order in the Space of Distribution Functions
23(12)
3.1 The Lorenz Curve
24(3)
3.2 The Lorenz Order
27(5)
3.3 Exercises
32(3)
4 Transformations and Their Effects
35(10)
4.1 Deterministic Transformations
35(3)
4.2 Stochastic Transformations
38(3)
4.3 Exercises
41(4)
5 Inequality Measures
45(70)
5.1 Introduction
45(1)
5.2 Common Measures of Inequality
46(5)
5.2.1 Seven Basic Inequality Measures
46(3)
5.2.2 Inequality Measures Based on the Concept of Entropy
49(2)
5.3 Inequality Measures Derived from the Lorenz Curve
51(18)
5.3.1 The Gini Index
51(3)
5.3.2 Generalizations of the Gini Index
54(2)
5.3.3 Decomposition of the Gini and Yitzhaki Indices
56(5)
5.3.4 Inequality Indices Related to Lorenz Curve Moments
61(2)
5.3.5 The Pietra Index
63(3)
5.3.6 The Palma Index and Income Share Ratios Inequality Indices
66(1)
5.3.7 The Amato Index
67(1)
5.3.8 The Elteto and Frigyes Inequality Measures
68(1)
5.4 The Atkinson and the Generalized Entropy Indices
69(8)
5.4.1 The Atkinson Indices
70(1)
5.4.2 The Generalized Entropy Indices and the Theil Indices
70(2)
5.4.3 Decomposability of Certain Indices
72(5)
5.5 Estimation with Partial Information
77(3)
5.5.1 Bounds on the Gini Index
77(1)
5.5.2 Parameter Identification Using the Mean and the Gini Index
78(2)
5.6 Moment Distributions
80(2)
5.7 Relations Between Inequality Measures
82(1)
5.8 Sample Versions of Analytic Measures of Inequality
83(26)
5.8.1 Absolute and Relative Mean Deviation and the Sample Pietra Index
83(2)
5.8.2 The Sample Amato and Bonferroni Indices
85(1)
5.8.3 The Sample Standard Deviation and Coefficient of Variation
86(1)
5.8.4 Gini's Mean Difference
87(2)
5.8.5 The Sample Gini Index
89(2)
5.8.6 Sample Lorenz Curve
91(2)
5.8.7 Bias of the Sample Lorenz Curve and Gini Index
93(4)
5.8.8 Asymptotic Distribution of Lorenz Ordinates and Income Shares
97(4)
5.8.9 The Elteto and Frigyes Indices
101(1)
5.8.10 Further Classical Sample Measures of Inequality
102(3)
5.8.11 The Sample Atkinson and Generalized Entropy Indices
105(3)
5.8.12 The Kolm Inequality Indices
108(1)
5.8.13 Additional Sample Inequality Indices
108(1)
5.9 A New Class of Inequality Measures
109(2)
5.10 Exercises
111(4)
6 Families of Lorenz Curves
115(30)
6.1 Basic Results
115(5)
6.1.1 A Characterization of the Lorenz Curve
116(1)
6.1.2 Lorenz Curves of Some Common Distributions
116(1)
6.1.3 Translated and Truncated Lorenz Curves
117(2)
6.1.4 The Modality of the Income Density Function
119(1)
6.2 The Alchemy of Lorenz Curves
120(2)
6.3 Parametric Families of Lorenz Curves
122(11)
6.3.1 Some Hierarchical Families
123(1)
6.3.2 General Quadratic Lorenz Curves
124(4)
6.3.3 Other Parametric Families
128(5)
6.4 Some Alternative Inequality Curves
133(8)
6.4.1 Generalized and Absolute Lorenz Curves
133(1)
6.4.2 Leimkuhler, Bonferroni and Zenga Curves
134(2)
6.4.3 Inequality Curves for the Lower and Middle Income Groups
136(3)
6.4.4 Reliability Curves
139(1)
6.4.5 Relative Deprivation
140(1)
6.5 Exercises
141(4)
7 Multivariate Majorization and Multivariate Lorenz Ordering
145(22)
7.1 Multivariate Majorization
145(3)
7.2 Multivariate Lorenz Orderings
148(7)
7.3 Explicit Expressions for the Arnold Lorenz Surface
155(5)
7.3.1 The Bivariate Sarmanov-Lee Lorenz Surface
157(3)
7.4 Summary Measures of m-Dimensional Inequality
160(2)
7.4.1 Bivariate Gini Index for the Arnold Lorenz Surface
161(1)
7.5 Alternative Multivariate Inequality Indices
162(3)
7.5.1 Multivariate Shannon and R6nyi Entropies
162(2)
7.5.2 Multivariate Generalized Entropy and Theil Indices
164(1)
7.6 Exercises
165(2)
8 Stochastic Majorization
167(10)
8.1 Definition and Main Results
167(8)
8.2 Exercises
175(2)
9 Some Related Orderings
177(10)
9.1 Star-Ordering
177(3)
9.2 Stochastic Dominance
180(4)
9.3 Exercises
184(3)
10 Inequality Analysis in Families of Income Distributions
187(24)
10.1 Introduction
187(1)
10.2 The McDonald Family: Definitions and Basic Properties
187(12)
10.2.1 Lorenz Curves and Gini Indices
191(4)
10.2.2 Other Inequality Measures
195(4)
10.3 The Generalized Pareto Distributions
199(5)
10.3.1 Lorenz Curves and Gini Indices
202(1)
10.3.2 Inequality Measures
202(2)
10.4 Stochastic Orderings Within the McDonald Family
204(4)
10.4.1 Introduction and the Orderings to be Used
204(1)
10.4.2 Comparisons for Two Distributions in the Same Subfamily of McDonald Distributions
205(2)
10.4.3 Comparisons for Two Distributions in Different McDonald Subfamilies
207(1)
10.5 Exercises
208(3)
11 Some Applications
211(20)
11.1 A Geometric Inequality of Cesaro
211(1)
11.2 Matrices with Prescribed Characteristic Roots
212(1)
11.3 Variability of Sample Medians and Means
213(2)
11.4 Reliability
215(1)
11.5 Genetic Selection
216(2)
11.6 Large Interactions
218(2)
11.7 Unbiased Tests
220(1)
11.8 Summation Modulo m
221(1)
11.9 Forecasting
222(3)
11.10 Ecological Diversity
225(2)
11.11 Covering a Circle
227(1)
11.12 Waiting for a Pattern
227(1)
11.13 Paired Comparisons
228(1)
11.14 Phase Type Distributions
229(1)
11.15 Gaussian Correlation
230(1)
12 More Applications
231(22)
12.1 Catchability
231(1)
12.2 Server Assignment Policies in Queueing Networks
232(1)
12.3 Disease Transmission
232(1)
12.4 Apportionment in Proportional Representation
233(1)
12.5 Connected Components in a Random Graph
234(1)
12.6 A Stochastic Relation Between the Sum and the Maximum of Two Random Variables
235(1)
12.7 Segregation
236(8)
12.8 Lorenz Order with Common Finite Support
244(2)
12.9 The Scarsini Dependence Order
246(7)
12.9.1 Extension to k Dimensions
250(3)
Bibliography 253(10)
Author Index 263(4)
Subject Index 267
Barry C. Arnold, PhD, is Distinguished Professor in the Statistics Department at the University of California, Riverside. He is a Fellow of the American Statistical Society, the American Association for the Advancement of Science, the Institute of Mathematical Statistics and is an elected member of the International Statistical Institute. He is the author of more than two hundred publications and eight books. José María Sarabia, PhD, is Professor of Statistics and Quantitative Methods in Business and Economics in the Department of Economics at the University of Cantabria, Spain. He is author of more than one hundred and fifty publications and ten books and is an associate editor of several journals including TEST, Communications in Statistics, and Journal of Statistical Distributions and Applications.