{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:44:00Z","timestamp":1760237040780,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,18]],"date-time":"2020-02-18T00:00:00Z","timestamp":1581984000000},"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>This paper studies a simple skewness measure to detect symmetry and asymmetry in samples. The statistic can be obviously applied with only three short central tendencies; i.e., the first and ninth deciles, and the median. The strength of the statistic to find symmetry and asymmetry is studied by employing numerous Monte Carlo simulations and is compared with some alternative measures by applying some simulation studies. The results show that the performance of this statistic is generally good in the simulation.<\/jats:p>","DOI":"10.3390\/sym12020296","type":"journal-article","created":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T04:18:29Z","timestamp":1582690709000},"page":"296","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["The Properties of a Decile-Based Statistic to Measure Symmetry and Asymmetry"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4686-0930","authenticated-orcid":false,"given":"Mohammad Reza","family":"Mahmoudi","sequence":"first","affiliation":[{"name":"Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam"},{"name":"Department of Statistics, Faculty of Science, Fasa University, Fasa, Fars 7461686131, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roya","family":"Nasirzadeh","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Science, Fasa University, Fasa, Fars 7461686131, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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, Ankara 06530, Turkey"},{"name":"Institute of Space Sciences, 077125 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0410-8839","authenticated-orcid":false,"given":"Kim-Hung","family":"Pho","sequence":"additional","affiliation":[{"name":"Fractional Calculus, Optimization and Algebra Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,18]]},"reference":[{"key":"ref_1","unstructured":"Sprinthall, R.C., and Fisk, S.T. 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Pharm."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/S1544-6123(03)00003-5","article-title":"On more robust estimation of skewness and kurtosis","volume":"1","author":"Kim","year":"2004","journal-title":"Financ. Res. Lett."},{"key":"ref_7","first-page":"154","article-title":"On location, scale, skewness and kurtosis of univariate distributions","volume":"1","author":"Oja","year":"1981","journal-title":"Scand J. Stat."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1214\/aoms\/1177731243","article-title":"A note on skewness and kurtosis","volume":"15","author":"Wilkins","year":"1944","journal-title":"Ann. 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Theory Methods"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/10691898.2010.11889493","article-title":"Investigating the investigative task: Testing for skewness\u2013An investigation of different test statistics and their power to detect skewness","volume":"18","author":"Tabor","year":"2010","journal-title":"J. Stat. Educ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1111\/j.1467-9574.1996.tb01502.x","article-title":"A simple measure of skewness","volume":"50","author":"Tajuddin","year":"1996","journal-title":"Stat. Neerl"},{"key":"ref_18","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_19","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_20","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_21","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_22","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. 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