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Tytuł książki

A unified Lorenz-type approach to divergence and dependence

Seria
Rozprawy Matematyczne tom/nr w serii: 335 wydano: 1994
Zawartość
Warianty tytułu
Abstrakty
EN

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
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 335
Liczba stron
54
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCXXXV
Daty
wydano
1994
otrzymano
1993-07-20
poprawiono
1994-01-28
Twórcy
  • Institute of Computer Science, Polish Academy of Sciences, P.O. Box 22, J. Ordona 21, 01-237 Warszawa, Poland
Bibliografia
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Języki publikacji
EN
Uwagi
1991 Mathematics Subject Classification: 62H30, 62H20, 90A19.
Identyfikator YADDA
bwmeta1.element.zamlynska-3f9b39c2-f5b5-4621-ab6d-71696fcd7fb6
Identyfikatory
ISSN
0012-3862
Kolekcja
DML-PL
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