Gini Inequality Index Methods and Applications

277 Pages·2021·3.855 MB·English

by  Nitis Mukhopadhyay, Partha Pratim Sengupta

“fm” — 2021/2/24 — 17:51 — page i — #1
Gini Inequality Index
“fm” — 2021/2/24 — 17:51 — page ii — #2
“fm” — 2021/2/24 — 17:51 — page iii — #3
Gini Inequality Index

Methods and Applications
Edited by

Nitis Mukhopadhyay and

Partha Pratim Sengupta
“fm” — 2021/2/24 — 17:51 — page iv — #4
First edition published 2021
by CRC Press
6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742
and by CRC Press
2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
©2021 selection and editorial matter, Nitis Mukhopadhyay and Partha Pratim Sengupta;
individual chapters, the contributors
CRC Press is an imprint of Taylor & Francis Group, LLC
The right of Nitis Mukhopadhyay and Partha Pratim Sengupta to be identified as the authors of
the editorial material, and of the authors for their individual chapters, has been asserted in
accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988.
Reasonable efforts have been made to publish reliable data and information, but the author and
publisher cannot assume responsibility for the validity of all materials or the consequences of
their use. The authors and publishers have attempted to trace the copyright holders of all
material reproduced in this publication and apologize to copyright holders if permission to
publish in this form has not been obtained. If any copyright material has not been
acknowledged please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted,
reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means,
now known or hereafter invented, including photocopying, microfilming, and recording, or in
any information storage or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, access
www.copyright.com or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood
Drive, Danvers, MA 01923, 978-750-8400. For works that are not available on CCC please
contact [email protected]
Trademark notice: Product or corporate names may be trademarks or registered trademarks and
are used only for identification and explanation without intent to infringe.
Library of Congress Cataloging -in -Publication Data
Names: Mukhopadhyay, Nitis, 1950-editor. |Pratim Sengupta, Partha, editor.
Title: Gini inequality index : methods and applications / edited by Nitis
Mukhopadhyay, Partha Pratim Sengupta.
Description: First edition. |Boca Raton : CRC Press, 2021. |Includes
bibliographical references and index.
Identifiers: LCCN 2020049874 (print) |LCCN 2020049875 (ebook) |ISBN
9780367688356 (hardback) |ISBN 9781003143642 (ebook)
Subjects: LCSH: Income distribution–Statistical methods. |Income
distribution–Mathematical methods. |Gini coefficient.
Classification: LCC HB523 .G566 2021 (print) |LCC HB523 (ebook) |DDC
339.201/5195–dc23
LC record available at https://lccn.loc.gov/2020049874
LC ebook record available at https://lccn.loc.gov/2020049875
ISBN: 978-0-367-68835-6 (hbk)
ISBN: 978-0-367-69869-0 (pbk)
ISBN: 978-1-00-314364-2 (ebk)
Typeset in Palatino
by MPS Limited
“fm” — 2021/2/24 — 17:51 — page v — #5
Presented with love to my granddaughter,
Saachi Elizabeth Mukhopadhyay, for the joy she brings.
Dadun: Nitis Mukhopadhyay
Presented to Aruna for giving me two precious gems:

Deep & Guria, my loving children.

Partha Pratim Sengupta
“fm” — 2021/2/24 — 17:51 — page vi — #6
“fm” — 2021/2/24 — 17:51 — page vii — #7
Contents
Foreword: Giovanni Maria Giorgi............................................................... ix

Foreword: Shelemyahu Zacks ..................................................................... xi

Foreword: Kanti V. Mardia ........................................................................ xiii

Preface ........................................................................................................ xv

Contributors ............................................................................................... xix

1. Introducing Informal Inequality Measures (IIMs)
Constructed from U-statistics of Degree Three or Higher
in Analyzing Economic Disparity ............................................................ 1
Nitis Mukhopadhyay and Bhargab Chattopadhyay
2. The Decomposition of the Gini Index Between and Within
Groups: A Key Factor in Gender Studies An Application in the
Context of Salary Distribution in Spain ............................................... 33
Beatriz Larraz, Encarnacion Moyano-Avila, and Jose M. Pavia
3. A Note on the Decomposition of Health Inequality by Population
Subgroups in the Case of Ordinal Variables ....................................... 53
Pundarik Mukhopadhaya and Jacques Silber
4. The Gini Index Decomposition and Overlapping Between
Population Subgroups ............................................................................. 63
Michele Costa
5. Gini’s Mean Difference-Based Minimum Risk Point
Estimator of Mean ..................................................................................... 93
Francis Bilson Darku and Bhargab Chattopadhyay
6. The Gini Concentration Index for the Study of Survival ............... 107

Marco Bonetti, Chiara Gigliarano, and Ugofilippo Basellini
7. An Axiomatic Analysis of Generalized Gini
Air Quality Indices ................................................................................. 125
Satya R. Chakravarty
vii
“fm” — 2021/2/24 — 17:51 — page viii — #8
viii Contents
8. Sequential Confidence Set and Point Estimation of
the Population Gini Index by Controlling Accuracies
Relative to the Population Mean ......................................................... 145
Nitis Mukhopadhyay, Shyamal K. De, and Tae Young Yang
9. A Test on Correlation Based on Gini’s Mean Difference ................ 171

Wolfgang Schmid and Ivan Semeniuk
10. Segregation Measures for Different Forms of Categorical
Data: Reinterpretation and Proposal ................................................... 191
Anjan Ray Chaudhury, Madhabendra Sinha,
and Partha Pratim Sengupta
11. Exploring Fixed-Accuracy Estimation for Population Gini
Inequality Index Under Big Data: A Passage to Practical
Distribution-Free Strategies .................................................................. 217
Nitis Mukhopadhyay
Index ......................................................................................................... 243
“fm” — 2021/2/24 — 17:51 — page ix — #9
Foreword
The research activity of Corrado Gini spanned many fields, from statistics
to economics, from demography to sociology and anthropology. His studies
on income and wealth, and above all on the measurement of the distribu-
tional inequality of these variables, gave him success and international fame
that remains still today. This type of research initially entered the political-
economic debate on how to achieve a more equitable distribution of income
and wealth, a debate which became particularly animated in the late 19th
and early 20th centuries. More than a century after its appearance in the lit-
erature the Gini index (G), also known as the Gini coefficient, Gini ratio, or
Gini concentration ratio, continues to be of interest to several scholars. The
topicality of this index is, in our opinion, due to its interpretative simplic-
ity and its application flexibility. The Gini index is of extreme relevance not
only in economics but in unbelievable fields at the time it was proposed.
Indeed, G has been used, inter alia, in geology, biomedicine, finance, insur-
ance, and criminology. For example, it has been used to detect the damage
caused by earthquakes, to investigate the distribution of proteins between
different cells, to study the distribution of citations to evaluate scientific pro-
ductivity of departments and universities, and also to measure and report
crime concentration.
Therefore, Prof. Nitis Mukhopadhyay and Prof. Partha Pratim Sengupta,
who edited this volume with great attention and rigor, have certainly carried
out noteworthy activities.
Giovanni Maria Giorgi
[email protected]
ix