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A unified Lorenz-type approach to divergence and dependence

100%

Kowalczyk T.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Introduction.......................................................................................................................................5 1. Divergence of probability measures................................................................................................8 1.1. Divergence of probability measures connected with two-class classification problems...............8 1.2. Concentration curve and its link with the Neyman-Pearson curve.............................................10 1.3. Divergence ordering $⪯_{NP}$.................................................................................................11 2. Link between divergence and inequality..........................................................................................13 2.1. Initial inequality axioms..............................................................................................................13 2.2. The Lorenz curve for nonnegative random variables..................................................................14 2.3. Inequality ordering $⪯_{L}$......................................................................................................15 2.4. Inequality versus divergence......................................................................................................17 2.5. Ratio variables...........................................................................................................................19 3. Link between divergence and dependence.....................................................................................20 3.1. Preliminary remarks...................................................................................................................20 3.2. Dependence ordering $⪯_{D}$................................................................................................22 3.3. Orderings related to $⪯_{D}$...................................................................................................22 4. Link between divergence and proportional representation.............................................................24 4.1. Formulation of the problem and definition of the ordering $⪯_{x}$..........................................24 4.2. Minimal elements for $⪯_{x}$...................................................................................................26 4.3. Maximal elements for $⪯_{x}$..................................................................................................29 5. Directed concentration of probability measures.............................................................................30 5.1. Directed concentration curve....................................................................................................30 5.2. Grade transformation of a random variable...............................................................................34 5.3. Correlation and ratio curves......................................................................................................35 5.4. Directed departure from proportionality....................................................................................40 6. Numerical measures relating to divergence....................................................................................42 6.1. Numerical inequality measures..................................................................................................42 6.2. Numerical measures of divergence............................................................................................44 6.3. Numerical measures of directed divergence..............................................................................45 6.4. Numerical measures of dependence..........................................................................................47 6.5. Numerical measures of departures from proportional representation.......................................49 References........................................................................................................................................51 Index of symbols................................................................................................................................54

Applications of monotonic dependence functions: descriptive aspects

49%

Kowalczyk T., Kowalski A., Matuszewski A., Pleszczyńska E.

Applicationes Mathematicae

1977-1980

tom 16

nr 4

579-591

Ograniczanie wyników

1 Applicationes Mathematicae

2 Kowalczyk T.

1 Kowalski A.

1 Matuszewski A.

1 Pleszczyńska E.

1 1994

1 1980

Wyniki wyszukiwania

A unified Lorenz-type approach to divergence and dependence

Applications of monotonic dependence functions: descriptive aspects