{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T20:49:34Z","timestamp":1778878174304,"version":"3.51.4"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T00:00:00Z","timestamp":1725235200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the IOAP of the University of Seville"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we present the unit-power half-normal distribution, derived from the power half-normal distribution, for data analysis in the open unit interval. The statistical properties of the unit-power half-normal model are described in detail. Simulation studies are carried out to evaluate the performance of the parameter estimators. Additionally, we implement the quantile regression for this model, which is applied to two real healthcare data sets. Our findings suggest that the unit power half-normal distribution provides a robust and flexible alternative for existing models for proportion data.<\/jats:p>","DOI":"10.3390\/axioms13090599","type":"journal-article","created":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T12:54:42Z","timestamp":1725281682000},"page":"599","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Unit-Power Half-Normal Distribution Including Quantile Regression with Applications to Medical Data"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-6161-2068","authenticated-orcid":false,"given":"Karol I.","family":"Santoro","sequence":"first","affiliation":[{"name":"Departamento de Estad\u00edstica y Ciencia de Datos, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8092-9666","authenticated-orcid":false,"given":"Yolanda M.","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Departamento de Estad\u00edstica, Facultad de Ciencias, Universidad del B\u00edo-B\u00edo, Concepci\u00f3n 4081112, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-3499-8967","authenticated-orcid":false,"given":"Darlin","family":"Soto","sequence":"additional","affiliation":[{"name":"Departamento de Estad\u00edstica, Facultad de Ciencias, Universidad del B\u00edo-B\u00edo, Concepci\u00f3n 4081112, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9064-2597","authenticated-orcid":false,"given":"Inmaculada","family":"Barranco-Chamorro","sequence":"additional","affiliation":[{"name":"Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Facultad de Matem\u00e1ticas, Universidad de Sevilla, 41012 Sevilla, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.stamet.2008.04.001","article-title":"Kumaraswamy\u2019s Distribution: A Beta-Type Distribution with Some Tractability Advantages","volume":"6","author":"Jones","year":"2009","journal-title":"Stat. Methodol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.insmatheco.2013.10.017","article-title":"The Log-Lindley distribution as an alternative to the beta regression model with applications in insurance","volume":"54","author":"Sordo","year":"2014","journal-title":"Insur. Math. Econ."},{"key":"ref_3","first-page":"53","article-title":"A new one-parameter unit Lindley distribution","volume":"1","author":"Mazucheli","year":"2019","journal-title":"Chil. J. Stat."},{"key":"ref_4","first-page":"142","article-title":"A new quantile regression model for modelling child mortality","volume":"10","author":"Seyam","year":"2022","journal-title":"Int. J. Biomath."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s00180-019-00921-y","article-title":"The unit-improved second-degree Lindley distribution: Inference and regression modelling","volume":"35","author":"Altun","year":"2020","journal-title":"Comput. Stat."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ahmad, H.H., Almetwally, E.M., Elgarhy, M., and Ramadan, D.A. (2023). On Unit Exponential Pareto Distribution for Modeling the Recovery Rate of COVID-19. Processes, 11.","DOI":"10.3390\/pr11010232"},{"key":"ref_7","first-page":"108","article-title":"On a Family of Distributions with Argument between 0 and 1 Obtained by Transformation of the Gamma Distribution and Derived Compound Distributions","volume":"19","author":"Grassia","year":"1977","journal-title":"J. Stat."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3423","DOI":"10.1080\/03610926.2018.1476717","article-title":"The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval","volume":"48","author":"Ghitany","year":"2018","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_9","first-page":"47","article-title":"The unit-Birnbaum-Saunders distribution with applications","volume":"1","author":"Mazucheli","year":"1977","journal-title":"Chil. J. Stat."},{"key":"ref_10","first-page":"579","article-title":"Unit Burr III distribution with application","volume":"23","author":"Modi","year":"2019","journal-title":"J. Stat. Manag. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s40314-021-01418-5","article-title":"On the unit Burr-XII distribution with the quantile regression modeling and applications","volume":"40","author":"Korkmaz","year":"2021","journal-title":"Comput. Appl. Math."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/s40745-020-00298-6","article-title":"Unit Modified Burr-III Distribution: Estimation, Characterizations and Validation Test","volume":"10","author":"Haq","year":"2023","journal-title":"Ann. Data Sci."},{"key":"ref_13","first-page":"271","article-title":"A flexible probability model for proportion data: Unit-half-normal distribution","volume":"7","author":"Bakouch","year":"2021","journal-title":"Commun. Stat. Case Stud. Data Anal."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"383","DOI":"10.2991\/jsta.2015.14.4.4","article-title":"Likelihood-based inference for the power half-normal distribution","volume":"14","author":"Bolfarine","year":"2015","journal-title":"J. Stat. Theory Appl."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Barrios, L., G\u00f3mez, Y.M., Venegas, O., Barranco-Chamorro, I., and G\u00f3mez, H.W. (2022). The Slashed Power Half-Normal Distribution with Applications. Mathematics, 10.","DOI":"10.3390\/math10091528"},{"key":"ref_16","first-page":"229","article-title":"The discrete Powe Half-Normal Distribution","volume":"82","author":"Pallini","year":"2022","journal-title":"Statistica"},{"key":"ref_17","first-page":"209","article-title":"Methods of measuring the concentration of wealth","volume":"9","author":"Lorenz","year":"1905","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_18","first-page":"1","article-title":"On the measurement of concentration and variability of characters","volume":"1","author":"Gini","year":"2005","journal-title":"Metron"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"124","DOI":"10.2307\/2223319","article-title":"Measurement of inequality of incomes","volume":"31","author":"Gini","year":"1921","journal-title":"Econ. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1214\/aos\/1176350046","article-title":"Skewness and Asymmetry: Measures and Orderings","volume":"14","author":"MacGillivray","year":"1986","journal-title":"Ann. Stat."},{"key":"ref_21","first-page":"25","article-title":"A quantile alternative for kurtosis","volume":"37","author":"Moors","year":"1988","journal-title":"J. R. Stat. Soc. Ser. D"},{"key":"ref_22","unstructured":"Balakrishnan, N., and Cohen, C.A. (1991). Order Statistics and Inference: Estimation Methods, Elsevier Science. Statistical Modeling and Decision Science."},{"key":"ref_23","unstructured":"Bonferroni, C.E. (1930). Elementi di Statistica Generale, Libreria Seber."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"419","DOI":"10.15446\/rce.v37n2spe.47947","article-title":"The Graphical Representation of Inequality","volume":"37","author":"Arcagni","year":"2014","journal-title":"Rev. Colomb. Estad."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1177\/0962280213497329","article-title":"Does Newton-Raphson really fail?","volume":"23","author":"MacDonald","year":"2014","journal-title":"Stat. Methods Med Res."},{"key":"ref_26","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_27","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1111\/j.2517-6161.1968.tb00724.x","article-title":"A general definition of residuals","volume":"30","author":"Cox","year":"1968","journal-title":"J. Royal Stat. Soc. Ser. B"},{"key":"ref_28","unstructured":"Bolar, K. (2024, April 01). STAT: Interactive Document for Working with Basic Statistical Analysis. Available online: https:\/\/cran.r-project.org\/web\/packages\/STAT\/index.html."},{"key":"ref_29","first-page":"25","article-title":"Unit-Gompertz Distribution with Applications","volume":"79","author":"Mazucheli","year":"2019","journal-title":"Statistica"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"41","DOI":"10.17713\/ajs.v50i3.1023","article-title":"Bias-Corrected Maximum Likelihood Estimators of the Parameters of the Unit-Weibull Distribution","volume":"50","author":"Mazucheli","year":"2021","journal-title":"Austrian J. Stat."},{"key":"ref_31","unstructured":"Menezes, A.F.B. (2024, April 15). unitquantreg: Parametric Quantile Regression Models for Bounded Data. Available online: https:\/\/cran.r-project.org\/web\/packages\/unitquantreg\/index.html."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1515\/ijb-2019-0163","article-title":"Multivariate quasi-beta regression models for continuous bounded data","volume":"17","author":"Petterle","year":"2021","journal-title":"Int. J. Biostat."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1038\/sj.bmt.1704926","article-title":"Association of post-thaw viable CD34+ cells and CFU-GM with time to hematopoietic engraftment","volume":"35","author":"Yang","year":"2005","journal-title":"Bone Marrow Transplant."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/9\/599\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:47:23Z","timestamp":1760111243000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/9\/599"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,2]]},"references-count":33,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["axioms13090599"],"URL":"https:\/\/doi.org\/10.3390\/axioms13090599","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,2]]}}}