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" Modelling and analysis of compositional data / "
Vera Pawlowsky-Glahn, Juan J. Egozcue, Raimon Tolosana-Delgado
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BL
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| Record Number
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640662
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dltt
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| Main Entry
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Pawlowsky-Glahn, Vera.
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| Title & Author
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Modelling and analysis of compositional data /\ Vera Pawlowsky-Glahn, Juan J. Egozcue, Raimon Tolosana-Delgado
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| Series Statement
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Statistics in practice
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| Page. NO
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1 online resource
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| ISBN
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9781119003137
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: 111900313X
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: 9781119003113
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: 1119003113
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: 9781119003144
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: 1119003148
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: 1118443063
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: 9781118443064
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9781118443064
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| Bibliographies/Indexes
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Includes bibliographical references and indexes
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| Contents
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Introduction -- Compositional Data and Their Sample Space -- Basic concepts -- Principles of compositional analysis -- Scale invariance -- Permutation invariance -- Subcompositional coherence -- Zeros, missing values, and other irregular components -- Kinds of irregular components -- Strategies to analyze irregular data -- Exercises -- The Aitchison Geometry -- General comments -- Vector space structure -- Inner product, norm and distance -- Geometric figures -- Exercises -- Coordinate Representation -- Introduction -- Compositional observations in real space -- Generating systems -- Orthonormal coordinates -- Balances -- Working on coordinates -- Additive logratio coordinates (alr) -- Orthogonal projections -- Matrix operations in the simplex -- Perturbation-linear combination of compositions -- Linear transformations of S<sup>D</sup>: endomorphisms -- Other matrix transformations on S<sup>D</sup>: nonlinear transformations -- Coordinates leading to alternative Euclidean structures -- Exercises -- Exploratory Data Analysis -- General remarks -- Sample center, total variance, and variation matrix -- Centering and scaling -- The biplot: a graphical display -- Construction of a biplot -- Interpretation of a 2D compositional biplot -- Exploratory analysis of coordinates -- A geological example -- Linear trends along principal components -- A nutrition example -- A political example -- Exercises -- Random Compositions -- Sample space -- Conventional approach to the sample space of compositions -- A compositional approach to the sample space of compositions -- Definitions related to random compositions -- Variability and center -- Probability distributions on the simplex -- The normal distribution on the simplex -- The Dirichlet distribution -- Other distributions -- Exercises -- Statistical Inference -- Point estimation of center and variability -- Testing hypotheses on compositional normality -- Testing hypotheses about two populations -- Probability and confidence regions for normal data -- Bayesian estimation with count data -- Exercises -- Linear Models -- Linear regression with compositional response -- Regression with compositional covariates -- Analysis of variance with compositional response -- Linear discrimination with compositional predictor -- Exercises -- Compositional Processes -- Linear processes -- Mixture processes -- Settling processes -- Simplicial derivative -- Elementary differential equations -- Constant derivative -- Forced derivative -- Complete first-order linear equation -- Harmonic oscillator -- Exercises -- Epilogue
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| Subject
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Multivariate analysis.
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Mathematical statistics.
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Geometric analysis.
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| Dewey Classification
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519.5/35
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| LC Classification
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QA278
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| Added Entry
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Egozcue, Juan J.,1950-
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Tolosana-Delgado, Raimon.
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| Added Entry
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Ohio Library and Information Network.
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