{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:43:51Z","timestamp":1760244231481,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2022,9,25]],"date-time":"2022-09-25T00:00:00Z","timestamp":1664064000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>One of the most accessible and useful statistical tools for comparing independent populations in different research areas is the coefficient of variation (CV). In this study, first, the asymptotic distribution of the ratio of CV of two uncorrelated populations is investigated. Then, the outputs are used to create a confidence interval and to establish a test of hypothesis about the CV ratio of the populations. The proposed approach is compared with an alternative method, showing its superiority and effectiveness.<\/jats:p>","DOI":"10.3390\/math10193495","type":"journal-article","created":{"date-parts":[[2022,9,26]],"date-time":"2022-09-26T01:41:58Z","timestamp":1664156518000},"page":"3495","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Improved Confidence Interval and Hypothesis Testing for the Ratio of the Coefficients of Variation of Two Uncorrelated Populations"],"prefix":"10.3390","volume":"10","author":[{"given":"Abbas","family":"Bahrampour","sequence":"first","affiliation":[{"name":"Department of Biostatistics and Epidemiology, Kerman University of Medical Sciences Research Center for Modeling in Health, Institute for Futures Studies in Health, Kerman 7616913555, Iran"}]},{"given":"Zeynab","family":"Avazzadeh","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Epidemiology, School of Public Health, Kerman University of Medical Sciences, Kerman 7616914115, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4686-0930","authenticated-orcid":false,"given":"Mohammad Reza","family":"Mahmoudi","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Science, Fasa University, Fasa 7461686131, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7359-4370","authenticated-orcid":false,"given":"Ant\u00f3nio M.","family":"Lopes","sequence":"additional","affiliation":[{"name":"LAETA\/INEGI, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Meng, Q., Yan, L., Chen, Y., and Zhang, Q. (2018). Generation of Numerical Models of Anisotropic Columnar Jointed Rock Mass Using Modified Centroidal Voronoi Diagrams. Symmetry, 10.","DOI":"10.3390\/sym10110618"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Aslam, M., and Aldosari, M.S. (2019). Inspection Strategy under Indeterminacy Based on Neutrosophic Coefficient of Variation. Symmetry, 11.","DOI":"10.3390\/sym11020193"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Iglesias-Caama\u00f1o, M., Carballo-L\u00f3pez, J., \u00c1lvarez-Yates, T., Cuba-Dorado, A., and Garc\u00eda-Garc\u00eda, O. (2018). Intrasession Reliability of the Tests to Determine Lateral Asymmetry and Performance in Volleyball Players. Symmetry, 10.","DOI":"10.3390\/sym10090416"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Ziegler, W.J. (1976). On an approximate test for homogeneity of coefficients of variation. Contribution to Applied Statistics, Birkhauser Verlag.","DOI":"10.1007\/978-3-0348-5513-6"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1080\/03610918608812532","article-title":"A simulation study of a test for the equality of the coefficients of variation","volume":"15","author":"Shafer","year":"1986","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1080\/03610918308812308","article-title":"A multi sample test for the equality of coefficients of variation in normal populations","volume":"12","author":"Doornbos","year":"1983","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_7","unstructured":"Hedges, L., and Olkin, I. (1985). Statistical Methods for Meta-Analysis, Academic Press."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1177\/0008068319920106","article-title":"On the performance of test for coefficient of variation","volume":"42","author":"Rao","year":"1992","journal-title":"Calcutta. Stat. Assoc. Bull."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1080\/03610929608831683","article-title":"Testing the equality of coefficients of variation in k normal populations","volume":"25","author":"Gupta","year":"1996","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_10","unstructured":"Rao, K.A., and Jose, C.T. (2001, January 22\u201329). Test for equality of coefficient of variation of k populations. Proceedings of the 53rd Session of International Statistical Institute, Seoul, Korea."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/S0377-0427(99)00312-X","article-title":"Use of R\u00e9nyi\u2019s divergence to test for the equality of the coefficient of variation","volume":"116","author":"Pardo","year":"2000","journal-title":"J. Comput. Appl. Math."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1081\/SAC-120017854","article-title":"Tests of coefficient of variation of normal population","volume":"32","author":"Nairy","year":"2003","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2187","DOI":"10.1080\/03610920701215126","article-title":"Confidence bounds and hypothesis tests for normal distribution coefficients of variation","volume":"36","author":"Verrill","year":"2007","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2621","DOI":"10.1007\/s00180-013-0421-x","article-title":"A parametric bootstrap approach for the equality of coefficients of variation","volume":"28","author":"Jafari","year":"2013","journal-title":"Comput. Stat."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1002\/(SICI)1097-0258(19960330)15:6<647::AID-SIM184>3.0.CO;2-P","article-title":"An asymptotic test for the equality of coefficients of variation from k normal populations","volume":"15","author":"Feltz","year":"1996","journal-title":"Stat. Med."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2003","DOI":"10.1002\/(SICI)1097-0258(19980915)17:17<2003::AID-SIM889>3.0.CO;2-I","article-title":"A simulation study comparing tests for the equality of coefficients of variation","volume":"17","author":"Fung","year":"1998","journal-title":"Stat. Med."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2213","DOI":"10.1002\/sim.2088","article-title":"Inferences on the common coefficient of variation","volume":"24","author":"Tian","year":"2005","journal-title":"Stat. Med."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1080\/03610920802187448","article-title":"Estimator and Tests for Common Coefficients of Variation in Normal Distributions","volume":"38","author":"Forkman","year":"2009","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1121","DOI":"10.1080\/00949651003724790","article-title":"A new generalized p-value approach for testing equality of coefficients of variation in k normal populations","volume":"81","author":"Liu","year":"2011","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/s00180-013-0445-2","article-title":"Improved tests for the equality of normal coefficients of variation","volume":"29","author":"Krishnamoorthy","year":"2013","journal-title":"Comput. Stat."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2630","DOI":"10.1080\/03610926.2013.788711","article-title":"Inferences on the coefficients of variation in a multivariate normal population","volume":"44","author":"Jafari","year":"2015","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"345","DOI":"10.2991\/jsta.2017.16.3.6","article-title":"Improved confidence intervals for the ratio of coefficients of variation of two lognormal distributions","volume":"16","author":"Hasan","year":"2017","journal-title":"J. Stat. Theory Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3529","DOI":"10.1080\/00949655.2018.1524894","article-title":"Accurate tests for the equality of coefficients of variation","volume":"88","author":"Shi","year":"2018","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1080\/03610919108812981","article-title":"Use of the squared ranks test to test for the equality of the coefficients of variation","volume":"20","author":"Miller","year":"1991","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"8575","DOI":"10.1080\/03610926.2016.1185118","article-title":"Inference on the ratio of two coefficients of variation of two lognormal distributions","volume":"46","author":"Nam","year":"2016","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"7173416","DOI":"10.1155\/2019\/7173416","article-title":"Improved Small Sample Inference on the Ratio of Two Coefficients of Variation of Two Independent Lognormal Distributions","volume":"2019","author":"Wong","year":"2019","journal-title":"J. Probab. Stat."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Yue, Z., and Baleanu, D. (2019). Inference about the Ratio of the Coefficients of Variation of Two Independent Symmetric or Asymmetric Populations. Symmetry, 11.","DOI":"10.3390\/sym11060824"},{"key":"ref_28","first-page":"87","article-title":"Large Sample Inference on the Ratio of Two Independent Binomial Proportions","volume":"5","author":"Haghbin","year":"2011","journal-title":"J. Math. Ext."},{"key":"ref_29","first-page":"83","article-title":"Inference on the Ratio of Variances of Two Independent Populations","volume":"7","author":"Mahmoudi","year":"2014","journal-title":"J. Math. Ext."},{"key":"ref_30","first-page":"71","article-title":"Inference on the Ratio of Correlations of Two Independent Populations","volume":"7","author":"Mahmoudi","year":"2014","journal-title":"J. Math. Ext."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1721","DOI":"10.1080\/03610926.2018.1438627","article-title":"On the Ratio of Two Independent Skewnesses","volume":"48","author":"Mahmoudi","year":"2019","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"366","DOI":"10.2991\/jsta.2017.16.3.8","article-title":"Large Sample Inference about the Ratio of Means in Two Independent Populations","volume":"16","author":"Mahmoudi","year":"2017","journal-title":"J. Stat. Theory Appl."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Ferguson Thomas, S. (1996). A Course in Large Sample Theory, Chapman & Hall.","DOI":"10.1007\/978-1-4899-4549-5"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"103868","DOI":"10.1016\/j.dib.2019.103868","article-title":"Compendium of hand, foot and mouth disease data in Malaysia from years 2010 to 2017","volume":"24","author":"Nelson","year":"2019","journal-title":"Data Brief"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"113370","DOI":"10.1016\/j.cam.2020.113370","article-title":"On kurtoses of two symmetric or asymmetric populations","volume":"391","author":"Mahmoudi","year":"2021","journal-title":"J. Comput. Appl. Math."}],"container-title":["Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-7390\/10\/19\/3495\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:39:06Z","timestamp":1760143146000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-7390\/10\/19\/3495"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,25]]},"references-count":35,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["math10193495"],"URL":"https:\/\/doi.org\/10.3390\/math10193495","relation":{},"ISSN":["2227-7390"],"issn-type":[{"type":"electronic","value":"2227-7390"}],"subject":[],"published":{"date-parts":[[2022,9,25]]}}}