UID:
kobvindex_GFZ1870429397
Umfang:
xvii, 247 Seiten
,
Diagramme
ISBN:
9781118443064
,
9781119003113
Serie:
Statistics in practice
Inhalt:
Cover -- Title Page -- Copyright -- Contents -- Preface -- About the Authors -- Acknowledgments -- Chapter 1 Introduction -- Chapter 2 Compositional Data and Their Sample Space -- 2.1 Basic concepts -- 2.2 Principles of compositional analysis -- 2.2.1 Scale invariance -- 2.2.2 Permutation invariance -- 2.2.3 Subcompositional coherence -- 2.3 Zeros, missing values, and other irregular components -- 2.3.1 Kinds of irregular components -- 2.3.2 Strategies to analyze irregular data -- 2.4 Exercises -- Chapter 3 The Aitchison Geometry -- 3.1 General comments -- 3.2 Vector space structure -- 3.3 Inner product, norm and distance -- 3.4 Geometric figures -- 3.5 Exercises -- Chapter 4 Coordinate Representation -- 4.1 Introduction -- 4.2 Compositional observations in real space -- 4.3 Generating systems -- 4.4 Orthonormal coordinates -- 4.5 Balances -- 4.6 Working on coordinates -- 4.7 Additive logratio coordinates (alr) -- 4.8 Orthogonal projections -- 4.9 Matrix operations in the simplex -- 4.9.1 Perturbation-linear combination of compositions -- 4.9.2 Linear transformations of SD: endomorphisms -- 4.9.3 Other matrix transformations on SD: nonlinear transformations -- 4.10 Coordinates leading to alternative Euclidean structures -- 4.11 Exercises -- Chapter 5 Exploratory Data Analysis -- 5.1 General remarks -- 5.2 Sample center, total variance, and variation matrix -- 5.3 Centering and scaling -- 5.4 The biplot: a graphical display -- 5.4.1 Construction of a biplot -- 5.4.2 Interpretation of a 2D compositional biplot -- 5.5 Exploratory analysis of coordinates -- 5.6 A geological example -- 5.7 Linear trends along principal components -- 5.8 A nutrition example -- 5.9 A political example -- 5.10 Exercises -- Chapter 6 Random Compositions -- 6.1 Sample space -- 6.1.1 Conventional approach to the sample space of compositions.
Anmerkung:
Description based on publisher supplied metadata and other sources
Sprache:
Englisch
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