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Data where for each entity and variable a distribution is given is called distributional data. In the era of "Big Data," this type of data is becoming more and more prevalent. This edited book presents a synthesis of research in this area over the last twenty years or so. It has been carefully edited to ensure it is consistent with respect to style, level, notation, etc. Each chapter includes real data examples to illustrate the topics and software where appropriate.
Preface
About the Editors
List of Figures
List of Tables
Contributors
Data Representation and Exploratory Analysis
Fundamental Concepts about Distributional Data
Descriptive Statistics based on Frequency Distribution
Descriptive Statistics for Numeric Distributional Data
The Quantile Methods to Analyze Distributional Data
Clustering and Classi cation
Partitive and Hierarchical Clustering of Distributional Datausing the Wasserstein Distance
Divisive Clustering of Histogram Data
Clustering of Modal Valued Data
Mixture Models for Distributional Data
Classication of Continuous Distributional Data Using the Logratio Approach
Dimension Reduction
Principal Component Analysis of Distributional Data
Principal Component Analysis of Numeric Distributional Data
Multidimensional Scaling of Distributional Data
Regression and Forecasting
Regression Analysis with the Distribution and Symmetric Distribution Model
Regression Analysis of Distributional Data Based on a Two-Component Model
Forecasting Distributional Time Series