“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. 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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