05562nam 2200745Ia 450 991101948610332120200520144314.09786612307805978128230780312823078009780470316979047031697797804703178150470317817(CKB)1000000000822228(EBL)470285(OCoLC)593219037(SSID)ssj0000336750(PQKBManifestationID)11223777(PQKBTitleCode)TC0000336750(PQKBWorkID)10283888(PQKB)10886227(MiAaPQ)EBC470285(PPN)159326133(Perlego)2757908(EXLCZ)99100000000082222819990615d2000 uy 0engur|n|---|||||txtccrDirectional statistics /Kanti V. Mardia, Peter E. Jupp[2nd ed.].Chichester ;New York Wileyc20001 online resource (452 p.)Wiley series in probability and statisticsDescription based upon print version of record.9780471953333 0471953334 Includes bibliographical references and index.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 Notation2.2 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 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 Series3.3.3 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 CYLINDER3.7.1 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 POPLLATIOX4.5.1 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 INTRODUCTION5.2 UNBIASED ESTIMATORS AND A CRAMER-RAO BOUNDPresents 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 matWiley series in probability and statistics.Distribution (Probability theory)Mathematical statisticsSampling (Statistics)Distribution (Probability theory)Mathematical statistics.Sampling (Statistics)519.5Mardia K. V12429Jupp Peter E55995MiAaPQMiAaPQMiAaPQBOOK9911019486103321Directional statistics104121UNINA