Analysis of Distributional Data

Paula Brito, Sonia Dias, Paula Brito, Sonia Dias

• Publisher: Chapman and Hall/CRC
• Year: 2022
• Print ISBN: 9781032255712
• eBook ISBN: 9781315353456
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

In a time when increasingly larger and complex data collections are being produced, it is clear that new and adaptive forms of data representation and analysis have to be conceived and implemented. Distributional data, i.e., data where a distribution rather than a single value is recorded for each descriptor, on each unit, come into this framework. Distributional data may result from the aggregation of large amounts of open/collected/generated data, or it may be directly available in a structured or unstructured form, describing the variability of some features. This book provides models and methods for the representation, analysis, interpretation, and organization of distributional data, taking into account its specific nature, and not relying on a reduction to single values, to be conform to classical paradigms.

Conceived as an edited book, gathering contributions from multiple authors, the book presents alternative representations and analysis' methods for distributional data of different types, and in particular,
-Uni- and bi-variate descriptive statistics for distributional data
-Clustering and classification methodologies
-Methods for the representation in low-dimensional spaces
-Regression models and forecasting approaches for distribution-valued variables

Furthermore, the different chapters
-Feature applications to show how the proposed methods work in practice, and how results are to be interpreted,
-Often provide information about available software.

The methodologies presented in this book constitute cutting-edge developments for stakeholders from all domains who produce and analyse large amounts of complex data, to be analysed in the form of distributions. The book is hence of interest for companies operating not only in the area of data analytics, but also on logistics, energy and finance. It also concerns national statistical institutes and other institutions at European and international level, where microdata is aggregated to preserve confidentiality and allow for analysis at the appropriate regional level. Academics will find in the analysis of distributional data a challenging up-to-date field of research.

Part IData Representation and Exploratory Analysis

1Fundamental Concepts about Distributional Data

DOI: 10.1201/​9781315370545-1

Sónia Dias

School of Technology and Management, Polytechnic Institute of Viana do Castelo & LIAAD-INESC TEC, Portugal

Paula Brito

Faculty of Economics, University of Porto & LIAAD-INESC TEC, Porto, Portugal

CONTENTS

1. 1.1 Introduction
2. 1.2 The framework of distributional data
   • 1.2.1 Definition and classification of symbolic variables
   • 1.2.2 Histogram-valued variables
3. 1.3 Operations with distributions
   • 1.3.1 Histogram Arithmetic
   • 1.3.2 Operations with Quantile Functions
4. 1.4 Distances between distributions
5. 1.5 Conclusion
   • Bibliography

In the classical data framework, one numerical value or one category is associated to each individual, such data is known as microdata. However, the interest of many studies is based on groups of records gathered according to a set of characteristics of the individuals, leading to macrodata. Symbolic Data Analysis (SDA) emerges with the aim to allow working with more complex data tables where the cells include more accurate and complete information. These cells may contain finite sets of values/categories, intervals, or distributions. The classification of the symbolic variables is defined according to the kind of observations. In distributional data we work with histogram-valued variables, where to each entity under analysis corresponds an empirical distributio...

Table of contents

• Cover Page
• Half-Title Page
• Title Page
• Copyright Page
• Contents
• Preface
• About the Editors
• List of Figures
• List of Tables
• Contributors
• I Data Representation and Exploratory Analysis
• II Clustering and Classification
• III Dimension Reduction
• IV Regression and Forecasting