{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:20:12Z","timestamp":1760145612733,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T00:00:00Z","timestamp":1722556800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Faisal University, Saudi Arabia","award":["GRANT KFU241133"],"award-info":[{"award-number":["GRANT KFU241133"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper explores bimodal skew-symmetric distributions, a versatile family of distributions characterized by parameters that control asymmetry and kurtosis. These distributions encapsulate both symmetrical and well-known asymmetrical behaviors. A simulation study evaluates the model\u2019s estimation accuracy, detailing the score function and the robustness of the observed information matrix, which is proven to be non-singular under specific conditions. We apply the bimodal skew-normal model to protein data from cancer cells, comparing its performance against four established distributions supported on the entire real line. Results indicate superior performance by the proposed model, underscoring its potential for enhancing analytical precision in biological research.<\/jats:p>","DOI":"10.3390\/sym16080985","type":"journal-article","created":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T16:14:58Z","timestamp":1722615298000},"page":"985","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Advanced Bimodal Skew-Symmetric Distributions: Methodology and Application to Cancer Cell Protein Data"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8557-3796","authenticated-orcid":false,"given":"Gadir","family":"Alomair","sequence":"first","affiliation":[{"name":"Department of Quantitative Methods, School Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7302-7461","authenticated-orcid":false,"given":"Hugo S.","family":"Salinas","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1531772, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3189-0670","authenticated-orcid":false,"given":"Hassan S.","family":"Bakouch","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Tanta University, Tanta 31111, Egypt"}]},{"given":"Idika E.","family":"Okorie","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Khalifa University, Abu Dhabi 127788, United Arab Emirates"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7772-0386","authenticated-orcid":false,"given":"Olayan","family":"Albalawi","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,2]]},"reference":[{"key":"ref_1","first-page":"171","article-title":"A class of distributions which includes the normal ones","volume":"12","author":"Azzalini","year":"1985","journal-title":"Scand. J. Stat."},{"key":"ref_2","first-page":"199","article-title":"Further results on a class of distributions which includes the normal ones","volume":"46","author":"Azzalini","year":"1986","journal-title":"Statistica"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1515\/rose.2002.10.2.133","article-title":"Some skew\u2013symmetric models","volume":"10","author":"Gupta","year":"2002","journal-title":"Random Oper. Stoch. Equ."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1111\/j.1467-9469.2004.03_007.x","article-title":"Flexible class of the skew-symmetric distributions","volume":"31","author":"Ma","year":"2004","journal-title":"Scand. J. Stat."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1465","DOI":"10.1081\/STA-120037254","article-title":"A new class of skew-normal distributions","volume":"33","author":"Quintana","year":"2004","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Pewsey, A. (2006). Some observations on a simple means of generating skew distributions. Advances in Distribution Theory, Order Statistics, and Inference Part of the Series Statistics for Industry and Technology, Springer.","DOI":"10.1007\/0-8176-4487-3_5"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"e1154","DOI":"10.1002\/cmm4.1154","article-title":"A new family of skewed distributions with application to some daily closing prices","volume":"3","author":"Bakouch","year":"2021","journal-title":"Comput. Math. Methods"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Salinas, H., Bakouch, H., Qarmalah, N., and Mart\u00ednez-Fl\u00f3rez, G. (2023). A flexible class of two-piece normal distribution with a regression illustration to biaxial fatigue data. Mathematics, 11.","DOI":"10.3390\/math11051271"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Khorsheed, E., Salinas, H.S., and Bakouch, H.S. (2020, January 26\u201327). A new family of skew-normal lifetime distributions for industrial applications. Proceedings of the 2020 International Conference on Data Analytics for Business and Industry: Way Towards a Sustainable Economy (ICDABI), Sakheer, Bahrain.","DOI":"10.1109\/ICDABI51230.2020.9325590"},{"key":"ref_10","unstructured":"Neymann, J. (1960, January 20\u201330). On measures of information and entropy. Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Los Angeles, CA, USA."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell. Syst. Tech. J."},{"key":"ref_12","unstructured":"R Core Team (2024). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing. Available online: https:\/\/www.R-project.org\/."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"\u00c7ankaya, M.N. (2018). Asymmetric bimodal exponential power distribution on the real line. Entropy, 20.","DOI":"10.3390\/e20010023"},{"key":"ref_14","first-page":"89","article-title":"Sulla determinazione empirica di una legge didistribuzione","volume":"4","author":"An","year":"1933","journal-title":"Giorn. Dell\u2019inst. Ital. Degli Att."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1214\/aoms\/1177730256","article-title":"Table for estimating the goodness of fit of empirical distributions","volume":"19","author":"Smirnov","year":"1948","journal-title":"Ann. Math. Stat."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"577","DOI":"10.18576\/jsap\/060313","article-title":"A new family of heavy tailed symmetric distribution for modeling financial data","volume":"6","author":"Nitha","year":"2017","journal-title":"J. Stat. Appl. Probab."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/8\/985\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:29:09Z","timestamp":1760110149000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/8\/985"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,2]]},"references-count":16,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["sym16080985"],"URL":"https:\/\/doi.org\/10.3390\/sym16080985","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,8,2]]}}}