Kanti V. Mardia
（1972年刊行，Academic Press［Probability and Mathematical Statistics］， ISBN:0124711502）
方向統計学（directional statistics）の古典．2000年に改訂版：Kanti V. Mardia & Peter E. Jupp『Directional Statistics』（2000年1月刊行，John Wiley & Sons，ISBN:0471953334→目次）が出ている．
【目次】
Preface vii
Introduction xviiChapter 1 — Angular data and frequency distributions
1. Introduction 1
2. Diagrammatical representation 1
3. Interrelations between different units of angular measurement 6
4. Forms of frequency distributions 9
5. Further examples of angular data 12Chapter 2 — Descriptive measures
1. Introduction 18
2. A measure of location 19
3. The circular variance 21
4. Calculations of the mean direction and the circular variance 25
5. Some other measures of location 28
6. Some other measures of dispersion 30
7. Trigonometric moments 35
8. Corrections for grouping 37Chapter 3 — Basic concepts and theoretical models
1. The distribution function 39
2. The characteristic function 41
3. Moments and measures of location and dispersion 44
4. Circular models 48
5. Angular distributions on the range (0, 2π/l) 69
6. Mixtures and multi-modal distributions 71
7. Circular standard deviation, skewness and kurtosis 74
8. Corrections for grouping 77Chapter 4 — Fundamental theorems and distribution theory
1. Introduction 80
2. Theorems on the characteristic function 80
3. Limit theorems 87
4. The isotropic random walk on the circle 93
5. Distributions of C, S and R for von Mises population 96
6. Distributions related to the multi-sample problem for von Mises population 99
7. Moments of R 105
8. The moments of C and R 108
9. Limiting distributions of angular statistics 110Chapter 5 — Point estimation
1. A Cramér-Rao type bound 118
2. The method of moments 120
3. Sufficiency 121
4. The von Mises distribution 122
5. A regression model 127
6. Mixtures of von Mises distibutions 128Chapter 6 — Tests for samples from von Mises populations
1. Introduction 131
2. Single sample tests 132
3. Two-sample tests 152
4. Multi-sample tests 162
5. A regression model 167
6. Tests for multi-modal and axial data 167Chapter 7 — Non-parametric tests
1. Introduction and basic results 171
2. Tests of goodness of fit and tests of uniformity 173
3. Tests of symmetry 195
4. Two-sample tests 196
5. Multi-sample tests 206
6. Tests for multi-modal and axial data 208Chapter 8 — Distributions on spheres
1. Spherical data 212
2. Other spherical co-ordinate systems 214
3. Azimuthal projections 215
4. Descriptive measures 218
5. Models 226
6. Distribution theory 236
7. Moments and limiting distributions 244
8. A distribution on a hypersphere 247Chapter 9 — Inference problems on the sphere
1. Introduction 249
2. Point estimation 249
3. Single sample tests 256
4. Two-sample tests 262
5. Multi-sample tests 267
6. A test for coplanarity 271
7. Tests for axial data 275
8. A review of some other tests and topics 281Appendix 1 — Bessel functions 287
Appendix 2 — Tables and charts for the circular case (abridged titles)
1. The von Mises distribution function 290
2. The population resultant length for the von Mises case 297
3. Maximum likelihood estimates for the von Mises case 298
4. A test of uniformity when the mean direction is known 299
5. Critical values for the Rayleigh test (circular case) 300
6. Percentage points of the von Mises distribution 301
7. Confidence interval for the mean direction 302
8. Confidence interval for the concentration parameter 304
9. Critical values for Watson-Williams' two-sample test 306
10. Critical values for Kuiper's test 308
11. Critical values for Hodges-Ajne's test 309
12. Critical values of the circular range 310
13. Critical values for the equal spacings test 311
14. Critical values for the uniform scores test 312
15. Critical values for Watson's two-sample tests 314
16. Critical values for the run test 315
17. Critical values for the multi-sample uniform scores test 316
18. Critical values for the bimodal scores test 317Appendix 3 — Tables and charts for the spherical case (abridged titles)
1. Percentage points of the Fisher distribution 320
2. Maximum likelihood estimates for the Fisher case 322
3. Maximum likelihood estimates for the Girdle case 323
4. Maximum likelihood estimates for the bipolar case 324
5. Critical values for the Rayleigh test (spherical case) 325
6. Critical values for testing a prescribed direction 326
7. Critical values for testing a prescribed concentration parameter 328
8. Critical values for Watson-Williams' two-sample test 329
Bibliography and Author Index 331
Subject Index 340
Index of Notation 356
