{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T10:30:10Z","timestamp":1766485810193,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,21]],"date-time":"2022-04-21T00:00:00Z","timestamp":1650499200000},"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>The class of skew normal distributions, introduced by Azzalini (1985), which is an asymmetric distribution and allows the presence of skewness. In this paper, we propose the pivotal quantity approach to construct the confidence interval for the mean, prediction interval for the mean of the future sample, and tolerance interval for the quantile. The fiducial distribution is also studied. Moreover, the performances of all the proposed confidence intervals are investigated through the Monte Carlo simulation. The pivotal quantity is a common method for calculating confidence intervals, which is used to construct confidence intervals in this paper. And the convergence of the obtained confidence interval is illustrated by the figures. Finally, a real data is used to explain proposed intervals in real life.<\/jats:p>","DOI":"10.3390\/sym14050855","type":"journal-article","created":{"date-parts":[[2022,4,21]],"date-time":"2022-04-21T03:46:11Z","timestamp":1650512771000},"page":"855","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Confidence Interval, Prediction Interval and Tolerance Interval for the Skew Normal Distribution: A Pivotal Approach"],"prefix":"10.3390","volume":"14","author":[{"given":"Xinlei","family":"Qi","sequence":"first","affiliation":[{"name":"The School of Cyberspace Security, Xi\u2019an University of Posts and Telecommunications, Xi\u2019an 710121, China"}]},{"given":"Huihui","family":"Li","sequence":"additional","affiliation":[{"name":"The Special Education School of Jinzhong City, Jinzhong 030600, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7379-9285","authenticated-orcid":false,"given":"Weizhong","family":"Tian","sequence":"additional","affiliation":[{"name":"College of Big Data and Internet, Shenzhen Technology University, Shenzhen 518118, China"}]},{"given":"Yaoting","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1017\/S0305004100016297","article-title":"Inverse probability","volume":"Volume 26","author":"Fisher","year":"1930","journal-title":"Mathematical Proceedings of the Cambridge Philosophical Society"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1993","DOI":"10.1016\/j.csda.2010.12.009","article-title":"Comparison of several means: A fiducial based approach","volume":"55","author":"Li","year":"2011","journal-title":"Comput. 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The Skew-Normal and Related Families, Cambridge University Press.","DOI":"10.1017\/CBO9781139248891"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1693","DOI":"10.1080\/02664763.2012.668177","article-title":"Large sample confidence intervals for the skewness parameter of the skew-normal distribution based on Fisher\u2019s transformation","volume":"39","author":"Mameli","year":"2012","journal-title":"J. Appl. Stat."},{"key":"ref_13","first-page":"191","article-title":"Estimation of Location Parameter in the Skew Normal Setting with Known Coefficient of Variation and Skewness","volume":"9","author":"Wang","year":"2016","journal-title":"Int. J. Intell. Technol. Appl. Stat."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wang, C., Wang, T., Trafimow, D., and Myuz, H.A. (2019). Desired sample size for estimating the skewness under skew normal settings. 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