| Preface to the first paperback edition | p. xiv |
| Preface | p. xv |
| The purpose of the book | p. xv |
| Survey of contents | p. xvi |
| How to use the book | p. xvii |
| Notation, terminology and conventions | p. xvii |
| Acknowledgements | p. xviii |
| Introduction | p. 1 |
| Descriptive methods | p. 15 |
| Introduction | p. 15 |
| Data display | p. 15 |
| Simple summary quantities | p. 30 |
| Sample trigonometric moments | p. 30 |
| Other measures of location and spread | p. 35 |
| Linear order statistics and circular ranks | p. 37 |
| Modifications for axial data | p. 37 |
| Models | p. 39 |
| Introduction | p. 39 |
| Notation; trigonometric moments | p. 40 |
| Probability density functions and distribution functions | p. 40 |
| Trigonometric moments and other population characteristics | p. 41 |
| Probability distributions on the circle | p. 43 |
| The uniform distribution U[superscript c] | p. 43 |
| The Cardioid distribution C([mu], [rho]) | p. 44 |
| Wrapped distributions--general | p. 45 |
| The Wrapped Cauchy distribution WC([mu], [rho]) | p. 46 |
| The Wrapped Normal distribution WN([mu], [rho]) | p. 47 |
| The von Mises distribution V M([mu], [kappa]) | p. 48 |
| Other models for circular data | p. 56 |
| Analysis of a single sample of data | p. 59 |
| Introduction | p. 59 |
| Exploratory analysis | p. 62 |
| Testing a sample of unit vectors for uniformity | p. 64 |
| Nonparametric methods for unimodal data | p. 72 |
| Introduction | p. 72 |
| Estimation of the median direction | p. 72 |
| Testing the median direction for a specified value | p. 73 |
| Estimation of the mean direction | p. 75 |
| Testing a mean direction for a specified value | p. 79 |
| Testing for symmetry | p. 80 |
| Statistical analysis of a random sample of unit vectors from a von Mises distribution | p. 81 |
| Introduction | p. 81 |
| Test for uniformity against a von Mises alternative | p. 82 |
| Goodness-of-fit for the von Mises model | p. 82 |
| Outlier test for discordancy for von Mises data | p. 85 |
| Parameter estimation for the von Mises distribution | p. 88 |
| Test for a specified mean direction or concentration parameter of a von Mises distribution | p. 93 |
| Statistical analysis of a random sample of unit vectors from a multimodal distribution | p. 96 |
| Fitting a mixture of two von Mises distributions | p. 97 |
| A test for the number of components in a mixture of von Mises distributions | p. 100 |
| Other topics | p. 102 |
| Analysis of two or more samples, and of other experimental layouts | p. 105 |
| Introduction | p. 105 |
| Exploratory analysis | p. 109 |
| Nonparametric methods for analysing two or more samples of unimodal data | p. 113 |
| Introduction | p. 113 |
| Test for a common median direction of two or more distributions | p. 114 |
| Estimation of the common median direction of two or more distributions | p. 114 |
| Test for a common mean direction of two or more distributions | p. 115 |
| Estimation of the common mean direction of two or more distributions | p. 118 |
| Test whether two or more distributions are identical | p. 122 |
| Analysis of two or more samples from von Mises distributions | p. 123 |
| Introduction | p. 123 |
| Test for a common mean direction of two or more von Mises distributions | p. 124 |
| Estimation of the common mean direction of two or more von Mises distributions | p. 130 |
| Test for equality of concentration parameters of two or more von Mises distributions | p. 131 |
| Estimation of the common concentration parameter of two or more von Mises distributions | p. 133 |
| Analysis of data from more complicated experimental designs | p. 133 |
| Correlation and regression | p. 135 |
| Introduction | p. 135 |
| Linear--circular association and circular--linear association | p. 139 |
| Introduction | p. 139 |
| Linear--circular association: C-association | p. 140 |
| Linear--circular association: C-linear association | p. 145 |
| Circular--circular association | p. 145 |
| Introduction | p. 145 |
| Circular--circular association: T-monotone association | p. 146 |
| Circular--circular association: T-linear association | p. 151 |
| A general test for circular--circular association | p. 153 |
| Regression models for a circular response variable | p. 155 |
| Introduction | p. 155 |
| Circular regression for the mean direction | p. 157 |
| Circular regression for the concentration parameter | p. 163 |
| Circular regression with a mixed model | p. 166 |
| Circular regression with a circular covariate | p. 168 |
| Analysis of data with temporal or spatial structure | p. 169 |
| Introduction | p. 169 |
| Analysis of temporal data | p. 172 |
| Introduction | p. 172 |
| Exploratory analysis | p. 173 |
| Detecting changes of direction and serial dependence | p. 176 |
| Fitting autoregressive models to time series | p. 184 |
| Spatial analysis | p. 189 |
| Some modern statistical techniques for testing and estimation | p. 199 |
| Introduction | p. 199 |
| Bootstrap methods for confidence intervals and hypothesis tests: general description | p. 200 |
| Bootstrap methods for circular data: confidence regions for the mean direction | p. 205 |
| Introduction | p. 205 |
| Methods for a single sample | p. 205 |
| Handling very small samples | p. 207 |
| Methods for combining two or more samples | p. 209 |
| Computing algorithms | p. 210 |
| Bootstrap methods for circular data: hypothesis tests for mean directions | p. 211 |
| Introduction | p. 211 |
| Methods for a single sample | p. 211 |
| Handling very small samples | p. 212 |
| Methods for comparing two or more samples | p. 213 |
| Randomisation, or permutation, tests | p. 214 |
| Tables | p. 219 |
| Percentiles of the Normal N(0,1) distribution | p. 219 |
| Percentiles of the X[superscript 2 subscript v]-distribution | p. 221 |
| Values of y = A[superscript -1 subscript 1] (x) for 0 [less than or equal] x [greater than or equal] 1 | p. 224 |
| Values of x = A[subscript 1] (y) for y [greater than or equal] 0 | p. 225 |
| Selected percentiles for the statistic V | p. 225 |
| Selected confidence intervals for the median direction | p. 226 |
| Critical values for the Wilcoxon signed-rank statistic | p. 227 |
| Critical values for testing goodness of fit of a von Mises distribution | p. 230 |
| Critical values for the discordancy test for a von Mises sample | p. 231 |
| Critical values for the angular--linear rank correlation statistic U[subscript n] | p. 231 |
| Assessment of significance of the angular--linear rank correlation coefficients [lambda subscript n] and [lambda subscript n,M] | p. 232 |
| Critical values for the angular--angular rank correlation coefficient [Delta subscript n] | p. 234 |
| Critical values for the angular--angular rank correlation coefficient [Pi subscript n] | p. 236 |
| Data sets | p. 239 |
| Arrival times at an intensive care unit | p. 239 |
| Long-axis orientations of feldspar laths | p. 240 |
| Movements of turtles | p. 241 |
| Directional preferences of starhead topminnows | p. 241 |
| Long-axis orientations of feldspar laths | p. 242 |
| Cross-bed azimuths of palaeocurrents | p. 242 |
| Movements of ants | p. 243 |
| Orientations of pebbles | p. 243 |
| Dance directions of bees | p. 244 |
| Directions of desert ants | p. 244 |
| Movements of sea stars | p. 245 |
| Vanishing directions of homing pigeons | p. 245 |
| Orientations of termite mounds | p. 246 |
| Seasonal wind directions | p. 249 |
| Groove and tool marks, and flute marks | p. 250 |
| Cross-bed measurements from Himalayan molasse | p. 250 |
| Orientations of rock cores | p. 251 |
| Wind direction and ozone concentration | p. 251 |
| Nest orientations and creek directions | p. 252 |
| Movements of blue periwinkles | p. 252 |
| Pairs of wind directions | p. 253 |
| Face-cleat in a coal seam | p. 254 |
| Wind directions | p. 254 |
| Time series of flare azimuths | p. 255 |
| References | p. 257 |
| Index | p. 269 |
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