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Gini coefficient
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== Other uses == Although the Gini coefficient is most popular in economics, it can, in theory, be applied in any field of science that studies a distribution. For example, in ecology, the Gini coefficient has been used as a measure of [[biodiversity]], where the cumulative proportion of species is plotted against the cumulative proportion of individuals.<ref name=natureArticle>{{cite journal | last1 = Wittebolle | first1 = Lieven | title = Initial community evenness favours functionality under selective stress | journal = [[Nature (journal)|Nature]] | year = 2009 | volume = 458 | issue = 7238 | pmid = 19270679 | pages = 623–626 | doi = 10.1038/nature07840| display-authors = 2 | last2 = Marzorati | first2 = Massimo | last3 = Balloi | first3 = Annalisa | last4 = Daffonchio | first4 = Daniele | last5 = Heylen | first5 = Kim | last6 = De Vos | first6 = Paul | last7 = Verstraete | first7 = Willy | last8 = Boon | first8 = Nico | bibcode = 2009Natur.458..623W | s2cid = 4419280 }}</ref> In health, it has been used as a measure of the inequality of health-related [[quality of life]] in a population.<ref name=popHealthArticle>{{cite journal | last=Asada | first=Yukiko | title = Assessment of the health of Americans: the average health-related quality of life and its inequality across individuals and groups | journal = Population Health Metrics | year = 2005 | volume = 3 | pmid=16014174 | page = 7 | pmc=1192818 | doi = 10.1186/1478-7954-3-7 | doi-access=free }}</ref> In education, it has been used as a measure of the inequality of universities.<ref name=MinervaArticle>{{cite journal | last1= Halffman | first1= Willem | last2= Leydesdorff | first2= Loet | title = Is Inequality Among Universities Increasing? Gini Coefficients and the Elusive Rise of Elite Universities | journal = Minerva | year = 2010 | volume = 48 | pmid= 20401157 | issue= 1 | pages = 55–72 | pmc= 2850525 | doi = 10.1007/s11024-010-9141-3| arxiv= 1001.2921 }}</ref> In chemistry it has been used to express the selectivity of [[protein kinase inhibitors]] against a panel of kinases.<ref name=JMedChemArticle>{{cite journal | last = Graczyk | first = Piotr | title = Gini Coefficient: A New Way To Express Selectivity of Kinase Inhibitors against a Family of Kinases | journal = Journal of Medicinal Chemistry | year = 2007 | volume = 50 | issue = 23 | pmid = 17948979 | pages = 5773–5779 | doi = 10.1021/jm070562u}}</ref> In engineering, it has been used to evaluate the fairness achieved by Internet routers in scheduling packet transmissions from different flows of traffic.<ref name=GreedyFairQueueing>{{Cite book |first1=Hongyuan |last1=Shi |first2=Harish |last2=Sethu |contribution=Greedy Fair Queueing: A Goal-Oriented Strategy for Fair Real-Time Packet Scheduling |pages=345–356 |title=Proceedings of the 24th IEEE Real-Time Systems Symposium |publisher=[[IEEE Computer Society]] |isbn=978-0-7695-2044-5 |year=2003}}</ref> In [[machine learning]], it has been used as a unified metric for evaluating many-versus-many (all-to-all) similarity in vector spaces across various data types, including images and text, and to show their effectiveness in guiding machine learning training sample selection, especially in sparse information settings.<ref>{{Citation | last1 = Fauber | first1 = Ben | title = Gini Coefficient as a Unified Metric for Evaluating Many-versus-Many Similarity in Vector Spaces. | date = 2024 | volume = abs/2411.07983 | arxiv = 2411.07983 }}</ref> The Gini coefficient is sometimes used for the measurement of the discriminatory power of [[credit rating|rating]] systems in [[credit risk]] management.<ref>{{cite book|title=The Analytics of Risk Model Validation (Quantitative Finance)|editor1-first=George A.|editor1-last=Christodoulakis|editor2-first=Stephen|editor2-last=Satchell|isbn=978-0-7506-8158-2|date=November 2007|publisher=Academic Press}}</ref> A 2005 study accessed US census data to measure home computer ownership and used the Gini coefficient to measure inequalities amongst whites and African Americans. Results indicated that although decreasing overall, home computer ownership inequality was substantially smaller among white households.<ref>{{cite journal|last1=Chakraborty|first1=J|last2=Bosman|first2=MM|title=Measuring the digital divide in the United States: race, income, and personal computer ownership|journal=Prof Geogr|year=2005|volume=57|issue=3|pages=395–410|doi=10.1111/j.0033-0124.2005.00486.x|bibcode=2005ProfG..57..395C|s2cid=154401826}}</ref> A 2016 peer-reviewed study titled Employing the Gini coefficient to measure participation inequality in treatment-focused Digital Health Social Networks<ref>{{cite journal|last1=van Mierlo|first1=T|last2=Hyatt|first2=D|last3=Ching|first3=A|title=Employing the Gini coefficient to measure participation inequality in treatment-focused Digital Health Social Networks|journal=Netw Model Anal Health Inform Bioinforma|date=2016|volume=5|issue=32|pages=32|doi=10.1007/s13721-016-0140-7|pmid=27840788|pmc=5082574}}</ref> illustrated that the Gini coefficient was helpful and accurate in measuring shifts in inequality, however as a standalone metric it failed to incorporate overall network size. Discriminatory power refers to a credit risk model's ability to differentiate between defaulting and non-defaulting clients. The formula <math>G_1</math>, in the calculation section above, may be used for the final model and at the individual model factor level to quantify the discriminatory power of individual factors. It is related to the accuracy ratio in population assessment models. The Gini coefficient has also been applied to analyze inequality in [[Online dating application|dating apps]].<ref>{{Cite web|last=worst-online-dater|date=2015-03-25|title=Tinder Experiments II: Guys, unless you are really hot you are probably better off not wasting your…|url=https://medium.com/@worstonlinedater/tinder-experiments-ii-guys-unless-you-are-really-hot-you-are-probably-better-off-not-wasting-your-2ddf370a6e9a|access-date=2021-04-28|website=Medium|language=en}}</ref><ref>{{Cite web|last=Kopf|first=Dan|title=These statistics show why it's so hard to be an average man on dating apps|url=https://qz.com/1051462/these-statistics-show-why-its-so-hard-to-be-an-average-man-on-dating-apps/|access-date=2021-04-28|website=Quartz|date=15 August 2017 |language=en}}</ref> Kaminskiy and Krivtsov<ref>{{cite book |last1= Kaminskiy |first1= M.P.|last2= Krivtsov|first2= V.V.|date= 2011|chapter= A Gini-Type Index for Aging/Rejuvenating Objects|title= Mathematical and Statistical Models and Methods in Reliability|location= Birkhäuser Boston|url = https://www.springer.com/gp/book/9780817649708| publisher= Springer|pages= 133–140|isbn=978-0-8176-4970-8}}</ref> extended the concept of the Gini coefficient from economics to [[reliability theory]] and proposed a Gini-type coefficient that helps to assess the degree of aging of non-repairable systems or aging and rejuvenation of repairable systems. The coefficient is defined between −1 and 1 and can be used in both empirical and parametric life distributions. It takes negative values for the class of decreasing failure rate distributions and point processes with decreasing failure intensity rate and is positive for the increasing failure rate distributions and point processes with increasing failure intensity rate. The value of zero corresponds to the [[Exponential distribution|exponential life distribution]] or the [[Poisson point process#Homogeneous Poisson point process|Homogeneous Poisson Process]].
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