Mardia / Birnbaum / Lukacs Statistics of Directional Data

1. Auflage 2014
ISBN: 978-1-4832-1866-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 380 Seiten, Web PDF

Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Statistics of Directional Data aims to provide a systematic account of statistical theory and methodology for observations which are directions. The publication first elaborates on angular data and frequency distributions, descriptive measures, and basic concepts and theoretical models. Discussions focus on moments and measures of location and dispersion, distribution function, corrections for grouping, calculation of the mean direction and the circular variance, interrelations between different units of angular measurement, and diagrammatical representation. The book then examines fundamental theorems and distribution theory, point estimation, and tests for samples from von Mises populations. The text takes a look at non-parametric tests, distributions on spheres, and inference problems on the sphere. Topics include tests for axial data, point estimation, distribution theory, moments and limiting distributions, and tests of goodness of fit and tests of uniformity. The publication is a dependable reference for researchers interested in probability and mathematical statistics.

Autoren/Hrsg.

Mardia, K. V.

Birnbaum, Z. W.

Lukacs, E.

Inhaltsverzeichnis

1;Front Cover;1
2;Statistics of Directional Data;4
3;Copyright Page;5
4;Table of Contents;14
5;Dedication;6
6;Preface;8
7;Introduction;18
8;Acknowledgements;12
9;Chapter 1. Angular data and frequency distributions;22
9.1;1. Introduction;22
9.2;2. Diagrammatical representation;22
9.3;3. Interrelations between different units of angular measurement;27
9.4;4. Forms of frequency distributions;30
9.5;5. Further examples of angular data;33
10;Chapter 2. Descriptive measures;39
10.1;1. Introduction;39
10.2;2. A measure of location;40
10.3;3. The circular variance;42
10.4;4. Calculation of the mean direction and the circular variance;46
10.5;5. Some other measures of location;49
10.6;6. Some other measures of dispersion;51
10.7;7. Trigonometric moments;56
10.8;8. Corrections for grouping;58
11;Chaapter 3. Basic concepts and theoretical models;60
11.1;1. The distribution function;60
11.2;2. The characteristic function;62
11.3;3. Moments and measures of location and dispersion;65
11.4;4. Circular models;69
11.5;5. Angular distributions on the range (0, 2p/l);90
11.6;6. Mixtures and multi-modal distributions;92
11.7;7. Circular standard deviation, skewness and kurtosis;95
11.8;8. Corrections for grouping;98
12;Chapter 4. Fundamental theorems and distribution theory;101
12.1;1. Introduction;101
12.2;2. Theorems on the characteristic function;101
12.3;3. Limit theorems;108
12.4;4. The isotropic random walk on the circle;114
12.5;5. Distributions of C, S and R for a von Mises population;117
12.6;6. Distributions related to the multi-sample problem for von Mises populations;120
12.7;7. Moments of R;126
12.8;8. The moments of C and S;129
12.9;9. Limiting distributions of angular statistics;131
13;Chapter 5. Point estimation;139
13.1;1. A Cramér-Rao type bound;139
13.2;2. The method of moments;141
13.3;3. Sufficiency;142
13.4;4. The von Mises distribution;143
13.5;5. A regression model;148
13.6;6. Mixtures of von Mises distributions;149
14;Chapter 6. Tests for samples from von Mises populations;152
14.1;1. Introduction;152
14.2;2. Single sample tests;153
14.3;3. Two-sample tests;173
14.4;4. Multi-sample tests;183
14.5;5. A regression model;188
14.6;6. Tests for multi-modal and axial data;188
15;Chapter 7. Non-parametric tests;192
15.1;1. Introduction and basic results;192
15.2;2. Tests of goodness of fit and tests of uniformity;194
15.3;3. Tests of symmetry;216
15.4;4. Two-sample tests;217
15.5;5. Multi-sample tests;227
15.6;6. Tests for multimodal and axial data;229
16;Chapter 8. Distributions on spheres;233
16.1;1. Spherical data;233
16.2;2. Other spherical co-ordinate systems;235
16.3;3. Azimuthal projections;236
16.4;4. Descriptive measures;239
16.5;5. Models;247
16.6;6. Distribution theory;257
16.7;7. Moments and limiting distributions;265
16.8;8. A distribution on a hypersphere;268
17;Chapter 9. Inference problems on the sphere;270
17.1;1. Introduction;270
17.2;2. Point estimation;270
17.3;3. Single sample tests;277
17.4;4. Two-sample tests;283
17.5;5. Multi-sample tests;288
17.6;6. A test for coplanarity;292
17.7;7. Tests for axial data;296
17.8;8. A review of some other tests and topics;302
18;Appendix 1: Bessel functions;308
19;Appendix 2: Tables and charts for the circular case (abridged titles);310
19.1;1. The von Mises distribution function;311
19.2;2. The population resultant length for the von Mises case;318
19.3;3. Maximum likelihood estimates for the von Mises case;319
19.4;4. A test of uniformity when the mean direction is known;320
19.5;5. Critical values for the Rayleigh test (circular case);321
19.6;6. Percentage points of the von Mises distribution;322
19.7;7. Confidence interval for the mean direction;323
19.8;8. Confidence interval for the concentration parameter;325
19.9;9. Critical values for Watson-William's two-sample test;327
19.10;10. Critical values for Kuiper's test;329
19.11;11. Critical values for Hodges-Ajne's test;330
19.12;12. Critical values of the circular range;331
19.13;13. Critical values for the equal spacings test;332
19.14;14. Critical values for the uniform scores test;333
19.15;15. Critical values for Watson's two-sample tests;335
19.16;16. Critical values for the run test;336
19.17;17. Critical values for the multi-sample uniform scores test;337
19.18;18. Critical values for the bimodal scores test;338
20;Appendix 3: Tables and charts for the spherical case (abridged titles);340
20.1;1. Percentage points of the Fisher distribution;341
20.2;2. Maximum likelihood estimates for the Fisher case;343
20.3;3. Maximum likelihood estimates for the Girdle case;344
20.4;4. Maximum likelihood estimates for the bipolar case;345
20.5;5. Critical values for the Rayleigh test (spherical case);346
20.6;6. Critical values for testing a prescribed direction;347
20.7;7. Critical values for testing a prescribed concentration parameter;349
20.8;8. Critical values for Watson-Williams' two-sample test;350
21;Bibliography and Author Index;352
22;Subject Index;361
23;Index of Notation;377