Introduction

Thomas Kämpke and Franz Josef Radermacher
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Thomas Kämpke: Research Institute for Applied Knowledge Processing (FAW/n)
Franz Josef Radermacher: University of Ulm

Chapter Chapter 1 in Income Modeling and Balancing, 2015, pp 3-8 from Springer

Abstract: Abstract An ad hoc definition of Lorenz curves is given for finite sample data. This ad hoc version of Lorenz curves can be understood as a purely deterministic concept. In order to extend this version to a much more general notion in later chapters, concepts from probability theory are briefly introduced. These include random events and their probabilities, σ-fields, measures, random variables, densities, distribution functions and expectations. Also, a simplified version of the inverse distribution function is given.Lorenz curves, inverse distribution functions and expectations form a triplet which will be used throughout. Basically, the expectation being finite ensures the existence of Lorenz curves.

Keywords: Probability Measure; Lorenz Curve; Support Point; Measurable Subset; Countable Additivity (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-13224-2_1

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