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E-raamat: Topics In Circular Statistics-vol 5

(Indian Statistical Inst, India), (Univ Of California, Santa Barbara, Usa)
  • Formaat: 336 pages
  • Sari: Series On Multivariate Analysis 5
  • Ilmumisaeg: 30-Apr-2001
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789814495240
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Topics In Circular Statistics-vol 5Suurem pilt
  • Formaat: 336 pages
  • Sari: Series On Multivariate Analysis 5
  • Ilmumisaeg: 30-Apr-2001
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789814495240
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This research monograph on circular data analysis covers some recent advances in the field, besides providing a brief introduction to, and a review of, existing methods and models. The primary focus is on recent research into topics such as change-point problems, predictive distributions, circular correlation and regression, etc. An important feature of this work is the S-plus subroutines provided for analyzing actual data sets. Coupled with the discussion of new theoretical research, the book should benefit both the researcher and the practitioner.
Introduction
1(25)
Introduction
1(3)
Applications and Background
4(5)
Some Examples
4(3)
The Need for Appropriate Analysis
7(2)
Descriptive Statistics
9(16)
Measure of Center
11(4)
Circular Distance and Measure of Dispersion
15(6)
Higher Moments
21(4)
Circular Probability Distributions
25(40)
Introduction
25(8)
Some Methods of Obtaining Circular Distributions
29(4)
Circular Distributions
33(19)
Uniform Distribution
33(1)
Cardioid Distribution
34(1)
A Triangular Distribution
34(1)
Circular Normal (CN) Distribution
35(8)
Offset Normal Distribution
43(1)
Wrapped Normal (WN) Distribution
44(1)
Wrapped Cauchy (WC) Distribution
45(1)
General Wrapped Stable (WS) Distributions
46(2)
Variations of the CN Distribution
48(2)
A Circular Beta Model
50(2)
Asymmetric Circular Distributions
52(1)
Bivariate Circular Distributions
52(2)
A Bivariate von Mises Distribution
52(1)
Wrapped Bivariate Normal Distribution
53(1)
Circular-Linear Distribution
53(1)
Generation of Circular Random Variables
54(2)
Appendix: Curved Exponential Families and CND
56(9)
Some Sampling Distributions
65(20)
Introduction
65(1)
Generalized Pearson's Random Walk Problem
66(4)
The General Case
67(3)
Sampling Distributions for CN Distribution
70(3)
Distribution of (C, S)
71(1)
Distribution of R
71(2)
Distribution of V
73(1)
Some Large Sample Results
73(7)
Series Approximations for R and V
74(1)
Central Limit Type Results
75(1)
Large Sample Results for Statistics Based on Moments
76(2)
First Significant Digit Phenomenon
78(2)
Two or More Samples
80(2)
Approximate Distributions for Large K
82(3)
Estimation of Parameters
85(22)
Introduction
85(1)
CN Distribution
85(5)
Estimating the Parameters of a CN Distribution
85(3)
Optimal Properties of the MLEs
88(2)
CN Mixtures
90(1)
ML Estimation for the WC Distribution
91(3)
Circular Beta Distribution
94(1)
WS Family
95(1)
Confidence Intervals
96(1)
Appendix: Proofs
97(10)
Tests for Mean Direction and Concentration
107(24)
Introduction
107(1)
Single Population
108(17)
Tests for Mean Direction
108(12)
Higher-Order Power Comparison
120(3)
Tests for the Concentration Parameter
123(2)
Two or More Populations
125(6)
Comparing Mean Directions and Approximate ANOVA
125(3)
Tests for Concentration Parameters
128(3)
Tests for Uniformity
131(20)
Introduction
131(1)
Uniformity against WS Alternatives
132(4)
LMP Test Against the WS Family
133(1)
Monotonicity of Power Function
134(1)
Consistency and Other Optimal Properties
135(1)
Uniformity versus WSM Alternatives
136(5)
Monotonicity of the Power Function
137(2)
Consistency and Other Optimal Properties
139(1)
Optimal Test with Unknown p
139(2)
LMP Invariant Test for Unknown μ
141(5)
Monotonicity of the Power Function
143(2)
Consistency and Other Optimal Properties
145(1)
Appendix: Proofs
146(5)
Nonparametric Testing Procedures
151(24)
Introduction
151(1)
One-Sample Problem and Goodness-of-fit
151(16)
Tests Based on Empirical Distribution Functions
152(5)
χ2 and Other Tests
157(4)
Tests Based on Sample Arc-Lengths
161(6)
Two-Sample Problems
167(4)
Two-Sample Tests based on Edf's
167(2)
Wheeler and Watson Test
169(1)
Tests based on Spacing-Frequencies
170(1)
Multi-Sample Tests
171(4)
Homogeneity Tests in Large Samples
172(3)
Circular Correlation and Regression
175(30)
Introduction
175(1)
A Circular Correlation Measure, ρc
176(7)
ρc for Some Parametric Models
180(3)
Rank Correlation
183(1)
Other Measures of Circular Correlation
184(2)
Circular-Linear Correlation
186(1)
Circular-Circular Regression
187(8)
Estimation of Regression Coefficients
188(3)
Determination of m
191(4)
Circular-Linear Regression
195(2)
Linear-Circular Regression
197(2)
Testing Stochastic Independence of Circular Variables
199(6)
Predictive Inference for Directional Data
205(12)
Introduction
205(2)
Prediction Under a von Mises Model
207(2)
Generalized von Mises-type Distributions
209(3)
l-Modal von Mises Distribution
209(3)
Bayesian Predictive Density
212(2)
Case of Large k
213(1)
Robustness Against Symmetric Wrapped Stable Family
214(1)
HPD Computation and An Example
215(2)
Outliers and Related Problems
217(24)
Introduction
217(1)
Diagnostic Tools
218(1)
Tests for Mixtures
219(13)
Introduction
219(2)
The LMPI Test
221(2)
Asymptotic Distribution of T
223(4)
Monotonicity and Consistency Properties
227(3)
Non-regular Cases
230(2)
Slippage Problem and Outliers
232(7)
Introduction
232(1)
A Decision Theoretic Approach
233(3)
The LRT
236(1)
Simulations and An Example
237(2)
Concluding Remarks
239(2)
Change-point Problems
241(26)
Introduction
241(2)
Tests for Change in Mean Direction
243(15)
k Known Case
243(2)
k Unknown Case
245(1)
Simulated Critical Values
246(9)
Power Comparisons
255(3)
Robustness
258(1)
Tests for Change in μ and/or k
258(2)
An Example
260(3)
Nonparametric Approaches
263(1)
Other Approaches
264(3)
Miscellaneous Topics
267(20)
Introduction
267(1)
An Entropy-based Test for the CND
267(5)
Classification and Discriminant Analysis
272(2)
Factorial Designs
274(4)
Likelihood Ratio Tests
276(2)
Bayesian Analysis
278(1)
Sequential Methods
279(1)
Shape Analysis
280(1)
Stochastic Processes and Time Series
280(2)
Density Estimation
282(1)
Periodic Smoothing Splines
283(4)
A Some Facts on Bessel Functions 287(4)
B How to Use the CircStats Package 291(4)
Installation Instructions for the CircStats Library
291(2)
Windows Version
291(1)
UNIX Version
292(1)
CircStats Functions
293(2)
Bibliography 295(16)
Author Index 311(4)
Subject Index 315(6)
Notations and Abbreviations Index 321
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