Statistics of Directional DataAcademic Press, 3 jul 2014 - 380 pagina's Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Statistics of Directional Data aims to provide a systematic account of statistical theory and methodology for observations which are directions. The publication first elaborates on angular data and frequency distributions, descriptive measures, and basic concepts and theoretical models. Discussions focus on moments and measures of location and dispersion, distribution function, corrections for grouping, calculation of the mean direction and the circular variance, interrelations between different units of angular measurement, and diagrammatical representation. The book then examines fundamental theorems and distribution theory, point estimation, and tests for samples from von Mises populations. The text takes a look at non-parametric tests, distributions on spheres, and inference problems on the sphere. Topics include tests for axial data, point estimation, distribution theory, moments and limiting distributions, and tests of goodness of fit and tests of uniformity. The publication is a dependable reference for researchers interested in probability and mathematical statistics. |
Inhoudsopgave
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| 18 | |
Chaapter 3 Basic concepts and theoretical models | 39 |
Chapter 4 Fundamental theorems and distribution theory | 80 |
Chapter 5 Point estimation | 118 |
Chapter 6 Tests for samples from von Mises populations | 131 |
Chapter 7 Nonparametric tests | 171 |
Chapter 8 Distributions on spheres | 212 |
Chapter 9 Inference problems on the sphere | 249 |
Bessel functions | 287 |
Tables and charts for the circular case abridged titles | 289 |
Tables and charts for the spherical case abridged titles | 319 |
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alternatives Appendix approximation axis Batschelet Beran Bessel function bimodal Cauchy distribution central limit theorem circular distributions circular mean circular variance combined sample concentration parameter conditional distribution confidence interval Consequently consider corresponding critical values data in Table data of Example defined density deviation direction cosines Equation Fisher distribution follows function Further given in Section Hence hypothesis of uniformity integral Io(k joint p.d.f. kind permission Kuiper's test large values likelihood function M(uo Mardia maximum likelihood estimate measure method Mises distribution mod 27t null distribution null hypothesis observations obtain order statistics plane polar co-ordinates problem R1 and R2 random sample random variable reduces respectively resultant length sample mean direction shown similar test sphere Stephens symmetric test of uniformity test the hypothesis test-statistic transformation two-sample test uniform distribution uniformly unimodal unimodal distributions unit circle Watson and Williams wind directions wrapped normal distribution zero direction