## Statistical Analysis of Circular DataData measured as angles or two-dimensional orientations are found almost everywhere in science. They commonly arise in biology, geography, geophysics, medicine, meteorology and oceanography, and many other areas. Examples of such data include departure directions of birds from release points, fracture plane orientations, the directional movement of animals after stimulation, wind and ocean current directions, and biorhythms. Statistical methods for handling such data have developed rapidly in the last twenty years, particularly data display, correlation, regression and analysis of tempered or spatially structured data. Further, some of the exciting modern developments in general statistical methodology, particularly nonparametric smoothing methods and bootstrap-based methods, have contributed significantly to relatively intractable data analysis problems. This book provides a unified and up-to-date account of techniques for handling circular data. |

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### Contents

I | 1 |

II | 15 |

III | 30 |

V | 35 |

VI | 37 |

VIII | 39 |

IX | 40 |

X | 41 |

LVIII | 153 |

LIX | 155 |

LX | 157 |

LXI | 163 |

LXII | 166 |

LXIII | 168 |

LXIV | 169 |

LXV | 172 |

XI | 43 |

XII | 44 |

XIII | 45 |

XIV | 46 |

XV | 47 |

XVI | 48 |

XVII | 56 |

XVIII | 59 |

XIX | 62 |

XX | 64 |

XXI | 72 |

XXIII | 73 |

XXIV | 75 |

XXV | 79 |

XXVI | 80 |

XXVII | 81 |

XXVIII | 82 |

XXX | 85 |

XXXI | 88 |

XXXII | 93 |

XXXIII | 96 |

XXXIV | 97 |

XXXV | 100 |

XXXVI | 102 |

XXXVII | 105 |

XXXVIII | 109 |

XXXIX | 113 |

XL | 114 |

XLII | 115 |

XLIII | 118 |

XLIV | 122 |

XLV | 123 |

XLVI | 124 |

XLVII | 130 |

XLVIII | 131 |

XLIX | 133 |

LI | 135 |

LII | 139 |

LIII | 140 |

LIV | 145 |

LVI | 146 |

LVII | 151 |

LXVI | 173 |

LXVII | 176 |

LXVIII | 184 |

LXIX | 189 |

LXX | 199 |

LXXI | 200 |

LXXII | 205 |

LXXIII | 207 |

LXXIV | 209 |

LXXV | 210 |

LXXVI | 211 |

LXXVII | 212 |

LXXVIII | 213 |

LXXIX | 214 |

LXXX | 219 |

LXXXI | 221 |

LXXXII | 224 |

LXXXIII | 225 |

LXXXV | 226 |

LXXXVI | 227 |

LXXXVII | 230 |

LXXXVIII | 231 |

XC | 232 |

XCI | 234 |

XCII | 239 |

XCIII | 240 |

XCIV | 241 |

XCVI | 242 |

XCVII | 243 |

XCIX | 244 |

CI | 245 |

CII | 246 |

CIII | 249 |

CIV | 250 |

CVI | 251 |

CVIII | 252 |

CIX | 253 |

CX | 254 |

CXII | 255 |

257 | |

269 | |

### Common terms and phrases

algorithm alternative Analysis Examples angular approximate association axial data binwidth bootstrap estimates bootstrap method bootstrap sample C-association calculate Cauchy distribution change-points circular data Circular dispersion circular random variable circular standard error common mean direction concentration parameter confidence interval confidence region correlation corresponding Critical values cross-bed data are listed data points data set defined density estimate display Fisher & Lee fracture given histogram large-sample linear data local regression Mardia mean resultant length measurements median Mises distribution Mises model Mises Q-Q plot modal groups multimodal noisy scrub birds nonparametric density estimate Normal distribution null hypothesis obtained outliers pooled estimate probability density function pseudo-random Q-Q plot random variable randomisation test rank CUSUM Re-sampling References and footnotes rose diagram sample mean direction sample of data sample sizes shown in Figure significance probability single sample small samples spatial Stage test statistic uniformity unimodal unimodal distribution von Mises distribution wind direction