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Record Nr. |
UNINA9911019486103321 |
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Autore |
Mardia K. V |
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Titolo |
Directional statistics / / Kanti V. Mardia, Peter E. Jupp |
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Pubbl/distr/stampa |
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Chichester ; ; New York, : Wiley, c2000 |
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ISBN |
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9786612307805 |
9781282307803 |
1282307800 |
9780470316979 |
0470316977 |
9780470317815 |
0470317817 |
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Edizione |
[[2nd ed.].] |
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Descrizione fisica |
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1 online resource (452 p.) |
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Collana |
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Wiley series in probability and statistics |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Distribution (Probability theory) |
Mathematical statistics |
Sampling (Statistics) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Directional Statistics; Contents; 11.1 INTRODIUCTION; Preface; 1 Circular Data; 1.1 INTRODUCTION; 1.2 DIAGR. AMMATICAL REPR.ESEXT.4TION; 1.2.1 Ungrouped Data; 1.2.2 Grouped Data; 1.2.3 Axial Data; 1.3 FORMS OF FREQUENCY DISTRIBUTIOSS; 1.3.1 Unimodal Distributions; 1.3.2 Multimodal Distributions; 1.4 FRTHER EXAMPLES OF DIRECTINAL DATA; 1.4.1 Earth Sciences; 1.4.2 Meteorology; 1.4.3 Biology; 1.4.4 Physics; 1.4.5 Psychology; 1.4.6 Image Analysis; 1.4.7 Medicine; 1.4.8 Astronomy; 1.5 Wrapping and Projecting; 2 Summary Statistics; 2.1. INTRODUCTION; 2.1.1 Preliminaries and Notation |
2.2 MEASUCRES OF LOCATION2.2.1 The Mean Direction; 2.2.2 The Metiiari Direr:tion; 2.3 MEASUR.ES OF CONCENTRATIOX AND DISPERSION; 2.3.1 The Mean Rwultant Length arid the Circular Variance; 2.3.2 Dworriposit.ion of Dispersion; 2.3.3 The Circirlw Standard Deviation; 2.3.4 Other M(xmres of Dispersion; 2.4 TRIGONOMETRIC I\IIOMEXTS; 2.4.1 Defiuitions; 2.4.2 Measures of Skewness mid |
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Kurtosis; 2.5 CORRECTIOKS FOR GROUPING; 3 Basic Concepts and Models; 3.1 INTRODUCTIOS; 3.2 THE DISTRIBUTIORT FUNCTIOIV; 3.3 THE CHARACTERISTlC FUXCTIOX; 3.3.1 Definition; 3.3.2 Fourier Series |
3.3.3 Indepeiidence and Convolution3.4 MOMESTS AND MEASURES OF LOCATION AND DISPERSIOS; 3.4.1 Trigonometric Moments; 3.4.2 Measures of Loration arid Dispersion; 3.4.3 A Chebysheu Inequality; 3.4.4 Symmetrical Dist.ribut.ions; 3.5 CIRCULAR MODELS; 3.5.1 Introduction; 3.5.2 Lattice Distributions; 3.5.3 Uniform Distribution; 3.5.4 Von Mises Distributions; 3.5.5 Carciioid Distributions; 3.5.6 Projwtrd Normal Distributions; 3.5.7 Wrapped Distributions; 3.6 MULTIPLY-WRAPPED DISTRIBUTIONS; 3.6.1 Wrapping the Circle rmtct Itself; 3.6.2 Mixtures; 3.7 DISTRIBUTIOKS ON THE TORUS AND THE CYLINDER |
3.7.1 Distributions on the Torus3.7.2 Distributions on the CyliIidrr; 4 Fundamental Theorems and Distribution Theory; 4.1 INTRODCCTION; 4.2 PROPERTIES OF CHARACTERISTIC FUNCTIOKS; 4.2.1 Key Properties; 4.2.2 Polnr Distributions mid Characteristic. FuIictions; 4.2.3 Further Properties of the Chwactcristir: Function; 4.3 LIMIT THEOREMS; 4.3.1 Central Linlit Theorems; 4.3.2 Poincar6's Theorem; 4.4 THE DISTRIBUTION OF # AND R FROM THE UNIFORM DISTRIBUTION; 4.4.1 The Distribution of 8 md R; 4.4.2 The Distribution of C and S; 4.5 DISTRIBUTION OF C, S AND R FOR A VON MISES POPLLATIOX |
4.5.1 The Joint Distribution of C and S4.5.2 Distributions of 8 and .; 4.5.3 hifarginal Distributions of C and S; 4.6 PROBLE~iFORVON~,~SESPOPUL.4TIOSS 4.6 DISTRIBUTIONS RELATED TO THE MULTI-SAhIPLE; 4.6.1 The Distribution of R; 4.6.2 The Joint Distribution of' (R, R); 4.6.3 Distributions for the Homogeneous Case; 4.7 MOMENTS OF R; 4.8 LIMITING DISTRIBUTIONS OF CIRCULAR . STATISTICS; 4.8.1 Large-Sample Approximations; 4.8.2 High-Concentration Approximations; 4.8.3 Furthtr Approximations to the Distribution of R; 5 Point Estimation; 5.1 INTRODUCTION |
5.2 UNBIASED ESTIMATORS AND A CRAMER-RAO BOUND |
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Sommario/riassunto |
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Presents new and up-dated material on both the underlying theory and the practical methodology of directional statistics, helping the reader to utilise and develop the techniques appropriate to their work.The book is divided into three parts. The first part concentrates on statistics on the circle. Topics covered include tests of uniformity, tests of good-of-fit, inference on von Mises distributions and non-parametric methods. The second part considers statistics on spheres of arbitrary dimension, and includes a detailed account of inference on the main distributions on spheres. Recent mat |
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