Statistical analysis circular data / N. I. Fisher

Incluye bibliografía: páginas 257-267 e índice: páginas 269-277

Preface to the first paperback edition.. Preface.. 1 The purpose of the book.. 2 Survey of contents.. 3 How to use the book.. 4 Notation, terminology and conventions.. 5 Acknowledgements.. 1 Introduction.. 2 Descriptive methods.. 2.1 Introduction.. 2.2 Data display.. 2.3 Simple summary quantities.. 2.3.1 Sample trigonometric moments.. 2.3.2 Other measures of location and spread.. 2.3.3 Linear order statistics and circular ranks.. 2.4 Modifications for axial data.. 3 Models.. 3.1 Introduction.. 3.2 Notation; trigonometric moments.. 3.2.1 Probability density functions and distribution functions.. 3.2.2 Trigonometric moments and other population characteristics.. 3.3 Probability distributions on the circle.. 3.3.1 The uniform distribution Uc.. 3.3.2 The Cardioid distribution C(μ,p.. 3.3.3 Wrapped distributions - general.. 3.3.4 The Wrapped Cauchy distribution WC(μ,p.. 3.3.5 The Wrapped Normal distribution WN(μ,p.. 3.3.6 The von Mises distribution VM(μ,K.. 3.3.7 Other models for circular data.. 4 Analysis of a single sample of data.. 4.1 Introduction.. 4.2 Exploratory analysis.. 4.3 Testing a sample of unit vectors for uniformity.. 4.4 Nonparametric methods for unimodal data.. 4.4.1 Introduction.. 4.4.2 Estimation of the median direction.. 4.4.3 Testing the median direction for a specified value.. 4.4.4 Estimation of the mean direction.. 4.4.5 Testing a mean direction for a specified value.. 4.4.6 Testing for symmetry.. 4.5 Statistical analysis of a random sample of unit vectors from a von Mises distribution.. 4.5.1 Introduction.. 4.5.2 Test for uniformity against a von Mises alternative.. 4.5.3 Goodness-of-fit for the von Mises model.. 4.5.4 Outlier test for discordancy for von Mises data.. 4.5.5 Parameter estimation for the von Mises distribution.. 4.5.6 Test for a specified mean direction or concentration parameter of a von Mises distribution.. 4.6 Statistical analysis of a random sample of unit vectors from a multimodal distribution

4.6.1 Fitting a mixture of two von Mises distributions.. 4.6.2 A test for the number of components in a mixture of von Mises distributions.. 4.7 Other topics.. 5 Analysis of two or more samples, and of other experimental layouts.. 5.1 Introduction.. 5.2 Exploratory analysis.. 5.3 Nonparametric methods for analysing two or more samples of unimodal data.. 5.3.1 Introduction.. 5.3.2 Test for a common median direction of two or more distributions.. 5.3.3 Estimation of the common median direction of two or more distributions.. 5.3.4 Test for a common mean direction of two or more distributions.. 5.3.5 Estimation of the common mean direction of two or more distributions.. 5.3.6 Test whether two or more distributions are identical.. 5.4 Analysis of two or more samples from von Mises distributions 123 5.4.1 Introduction.. 5.4.2 Test for a common mean direction of two or more von Mises distributions.. 5.4.3 Estimation of the common mean direction of two or more distributions.. 5.3.6 Test whether two or more distributions are identical.. 5.4 Analysis of two or more samples from von Mises distributions 123 5.4.1 Introduction.. 5.4.2 Test for a common mean direction of two or more von Mises distributions.. 5.4.3 Estimation of the common mean direction of two or more von Mises distributions.. 5.4.4 Test for equality of concentration parameters of two or more von Mises distributions.. 5.4.5 Estimation of the common concentration parameter of two or more von Mises distributions.. 5.5 Analysis of data from more complicated experimental designs.. 6 Correlation and regression.. 6.1 Introduction.. 6.2 Linear-circular association and circular-linear association 139 6.2.1 Introduction.. 6.2.2 Linear-circular association: C-association.. 6.2.3 Linear-circular association: C-linear association.. 6.3 Circular-circular association.. 6.3.1 Introduction.. 6.3.2 Circular-circular association: T-monotone association

6.3.3 Circular-circular association: T-linear association.. 6.3.4 A general test for circular-circular association.. 6.4 Regression models for a circular response variable.. 6.4.1 Introduction.. 6.4.2 Circular regression for the mean direction.. 6.4.3 Circular regression for the concentration parameter.. 6.4.4 Circular regression with a mixed model.. 6.4.5 Circular regression with a circular covariate.. 7 Analysis of data with temporal or spatial structure.. 7.1 Introduction.. 7.2 Analysis of temporal data.. 7.2.1 Introduction.. 7.2.2 Exploratory analysis.. 7.2.3 Detecting changes of direction and serial dependence.. 7.2.4 Fitting autoregressive models to time series.. 7.3 Spatial analysis.. 8 Some modern statistical techniques for testing and estimation.. 8.1 Introduction.. 8.2 Bootstrap methods for confidence intervals and hypothesis tests: general description.. 8.3 Bootstrap methods for circular data: confidence regions for the mean direction.. 8.3.1 Introduction.. 8.3.2 Methods for a single sample.. 8.3.3 Handling very small samples.. 8.3.4 Methods for combining two or more samples.. 8.3.5 Computing algorithms.. 8.4 Bootstrap methods for circular data: hypothesis tests for mean directions.. 8.4.1 Introduction.. 8.4.2 Methods for a single sample.. 8.4.3 Handling very small samples.. 8.4.4 Methods for comparing two or more samples.. 8.5 Randomisation, or permutation, tests.. Appendix A Tables.. A.1 Percentiles of the Normal N: p. ,1 distribution.. A.2 Percentiles of the Х²ѵ-distribution.. A.3 Values of y = A1-¹(x for 0 < x < 1.. A.4 Values of x = A1 (y for y > 0.. A.5 Selected percentiles for the statistic V.. A.6 Selected confidence intervals for the median direction.. A.7 Critical values for the Wilcoxon signed-rank statistic.. A.8 Critical values for testing goodness of fit of a von Mises distribution.. A.9 Critical values for the discordancy test for a von Mises samples

A. 10 Critical values for the angular-linear rank correlation statistic Uп.. A. 11 Assessment of significance of the angular-linear rank correlation coefficients λn and λn,M.. A. 12 Critical values for the angular-angular rank correlation coefficient Δn.. A. 13 Critical values for the angular-angular rank correlation coefficient Πn.. Appendix B Data sets.. B.l Arrivai times at an intensive care unit.. B.2 Long-axis orientations of feldspar laths.. B.3 Movements of turtles.. B.4 Directional preferences of starhead topminnows.. B.5 Long-axis orientations of feldspar laths.. B.6 Cross-bed azimuths of palaeocurrents.. B.7 Movements of ants.. B.8 Orientations of pebbles.. B.9 Dance directions of bees.. B.10 Directions of desert ants.. B.ll Movements of sea stars.. B.l2 Vanishing directions of homing pigeons.. B.l3 Orientations of termite mounds.. B.14 Seasonal wind directions.. B.l5 Groove and tool marks, and flute marks.. B.l6 Cross-bed measurements from Himalayan molasse.. B.l7 Orientations of rock cores.. B.l8 Wind direction and ozone concentration.. B.19 Nest orientations and creek directions.. B.20 Movements of blue periwinkles.. B.21 Pairs of wind directions.. B.22 Face-cleat in a coal seam.. B.23 Wind directions.. B.24 Time series of flare azimuths.. References.. Index

Data measured in the form of angles or two-dimensional orientations are to be found almost everywhere throughout science. They commonly arise in biology, geography, geophysics, medicine, meteorology and oceanography, as well as many other areas. Typical examples of such data include the departure directions of birds from points of release, orientations of fracture planes, the directional movement of animals in response to stimuli, directions of wind and ocean currents, and biorhythms. Statistical methods for handling such data have developed rapidly in the last 20 years, with emphasis on problems of data display, and the correlation, regression and analysis of data with temporal or spatial structure. In addition, some of the exciting modern developments in general statistical methodology, particularly nonparametric smoothing methods and bootstrap-based methods, have contributed significantly to the data analyst's ability to make progress with problems that have been relatively intractable. This book provides a unified and up-to-date account of techniques for handling circular data. eng