{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:41:04Z","timestamp":1760240464867,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,21]],"date-time":"2019-06-21T00:00:00Z","timestamp":1561075200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Coefficient of variation (CV) is a simple but useful statistical tool to make comparisons about the independent populations in many research areas. In this study, firstly, we proposed the asymptotic distribution for the ratio of the CVs of two separate symmetric or asymmetric populations. Then, we derived the asymptotic confidence interval and test statistic for hypothesis testing about the ratio of the CVs of these populations. Finally, the performance of the introduced approach was studied through simulation study.<\/jats:p>","DOI":"10.3390\/sym11060824","type":"journal-article","created":{"date-parts":[[2019,6,21]],"date-time":"2019-06-21T11:54:31Z","timestamp":1561118071000},"page":"824","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Inference about the Ratio of the Coefficients of Variation of Two Independent Symmetric or Asymmetric Populations"],"prefix":"10.3390","volume":"11","author":[{"given":"Zhang","family":"Yue","sequence":"first","affiliation":[{"name":"Teaching and Research Section of Public Education, Hainan Radio and TV University, No.20 Haidianerxi Road, Meilan District, Haikou 570208, Hainan, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Art and Sciences, Cankaya University, 0630 Ankara, Turkey"},{"name":"Institute of Space Sciences, 077125 Magurele-Bucharest, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,21]]},"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":"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_6","unstructured":"Hedges, L., and Olkin, I. (1985). Statistical Methods for Meta-Analysis, Academic Press."},{"key":"ref_7","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_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 coefficientsof 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","unstructured":"Wong, A., and Jiang, L. (2019). Improved Small Sample Inference on the Ratio of Two Coefficients of Variation of Two Independent Lognormal Distributions. J. Probab. Stat.","DOI":"10.1155\/2019\/7173416"},{"key":"ref_27","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_28","first-page":"83","article-title":"Inferrence on the Ratio of Variances of Two Independent Populations","volume":"7","author":"Mahmoudi","year":"2014","journal-title":"J. Math. Ext."},{"key":"ref_29","first-page":"71","article-title":"Inferrence on the Ratio of Correlations of Two Independent Populations","volume":"7","author":"Mahmoudi","year":"2014","journal-title":"J. Math. Ext."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1007\/s40995-017-0288-8","article-title":"Testing the Difference between Two Independent Time Series Models","volume":"41","author":"Mahmouudi","year":"2017","journal-title":"Iran. J. Sci. Technol. Trans. A Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"6284","DOI":"10.1080\/03610926.2014.960584","article-title":"Testing the Difference between Two Independent Regression Models","volume":"45","author":"Mahmoudi","year":"2016","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Mahmoudi, M.R., Nasirzadeh, R., and Mohammadi, M. (2018). On the Ratio of Two Independent Skewnesses. Commun. Stat. Theory Methods, in press.","DOI":"10.1080\/03610926.2018.1438627"},{"key":"ref_33","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_34","unstructured":"Mahmoudi, M.R. (2018). On Comparing Two Dependent Linear and Nonlinear Regression Models. J. Test. Eval., in press."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Mahmoudi, M.R., Heydari, M.H., and Avazzadeh, Z. (2018). Testing the difference between spectral densities of two independent periodically correlated (cyclostationary) time series models. Commun. Stat. Theory Methods, in press.","DOI":"10.1080\/03610926.2018.1472776"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.dsp.2018.07.004","article-title":"On the asymptotic distribution for the periodograms of almost periodically correlated (cyclostationary) processes","volume":"81","author":"Mahmoudi","year":"2018","journal-title":"Digit. Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.matcom.2018.12.008","article-title":"A new method to compare the spectral densities of two independent periodically correlated time series","volume":"160","author":"Mahmoudi","year":"2018","journal-title":"Math. Comput. Simul."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Mahmoudi, M.R., Mahmoodi, M., and Pak, A. (2019). On comparing, classifying and clustering several dependent regression models. J. Stat. Comput. Sim., in press.","DOI":"10.1080\/00949655.2019.1615489"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1569","DOI":"10.1007\/s00180-016-0705-z","article-title":"A New Method to Detect Periodically Correlated Structure","volume":"32","author":"Mahmoudi","year":"2017","journal-title":"Comput. Stat."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2919","DOI":"10.1080\/03610926.2017.1343847","article-title":"Testing the Equality of Two Independent Regression Models","volume":"47","author":"Mahmoudi","year":"2018","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Ferguson, T.S. (1996). A Course in Large Sample Theory, Chapman & Hall.","DOI":"10.1007\/978-1-4899-4549-5"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/6\/824\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:00:19Z","timestamp":1760187619000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/6\/824"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,21]]},"references-count":41,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2019,6]]}},"alternative-id":["sym11060824"],"URL":"https:\/\/doi.org\/10.3390\/sym11060824","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,6,21]]}}}