{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:45:21Z","timestamp":1760150721722,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,26]],"date-time":"2023-12-26T00:00:00Z","timestamp":1703548800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research, Qassim University, Saudi Arabia"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The current study addresses the estimation of the default parameters of alpha power-transformed power (APTPO) distributions. For the location and scale parameters of the APTPO distributions, we provide coefficients for both the best linear unbiased estimators (BLUE) and the best linear invariant estimators (BLIE) methods. Furthermore, we establish a forecast for future records. The parameters of the APTPO distribution are estimated using the maximum likelihood estimation method (MLE). The goodness-of-fit test (using Akaike information criterion (AIC)) is computed using both the inter-record time sequence and the entire sample. Also, we utilize a simulation approach to demonstrate the practicality and benefits of our perspective. Finally, we demonstrate the accuracy of these parameters and the performance of estimators through a real-life example.<\/jats:p>","DOI":"10.3390\/sym16010030","type":"journal-article","created":{"date-parts":[[2023,12,26]],"date-time":"2023-12-26T04:40:44Z","timestamp":1703565644000},"page":"30","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Different Methods for Estimating Default Parameters of Alpha Power-Transformed Power Distributions Using Record-Breaking Data"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3246-1293","authenticated-orcid":false,"given":"Rasha Abd El-Wahab","family":"Attwa","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1466-8821","authenticated-orcid":false,"given":"Taha","family":"Radwan","sequence":"additional","affiliation":[{"name":"Department of Management Information Systems, College of Business Administration, Qassim University, Buraydah 52571, Saudi Arabia"},{"name":"Department of Mathematics and Statistics, Faculty of Management Technology and Information Systems, Port Said University, Port Said 42521, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1111\/j.2517-6161.1952.tb00115.x","article-title":"The Distribution and Frequency of Record Values","volume":"14","author":"Chandler","year":"1952","journal-title":"J. R. Stat. Soc. Ser. B"},{"unstructured":"Feller, W. (1965). An Introduction to Probability Theory and Its Application, John Wiley & Sons, Inc.","key":"ref_2"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1002\/nav.3800330317","article-title":"On Estimating Population Characteristics from Record-Breaking Observations. I. Parametric Results","volume":"33","author":"Samaniego","year":"1986","journal-title":"Nav. Res. Logist. Q."},{"doi-asserted-by":"crossref","unstructured":"Gulati, S., and Padgett, W.J. (2003). Parametric and Nonparametric Inference from Record-Breaking Data, Springer.","key":"ref_4","DOI":"10.1007\/978-0-387-21549-5"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"20","DOI":"10.3390\/sym12010020","article-title":"Statistical Inference for the Weibull Distribution Based on \u03b4-Record Data","volume":"12","author":"Raul","year":"2019","journal-title":"Symmetry"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/BF02480340","article-title":"Linear Prediction of Record Values for the Two Parameter Exponential Distribution","volume":"32","author":"Ahsanullah","year":"1980","journal-title":"Ann. Inst. Stat. Math."},{"key":"ref_7","first-page":"103","article-title":"Record Values from Inverse Weibull Distribution and Associated Inference","volume":"16","author":"Nigm","year":"2007","journal-title":"J. Appl. Stat."},{"unstructured":"Johnson, N.L., Kotz, S., and Balakrishnan, N. (1994). Continuous Univariate Distributions-I, John Wiley.","key":"ref_8"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6543","DOI":"10.1080\/03610926.2015.1130839","article-title":"A new method of generating distribution with an application to exponential distribution with an application to exponential distribution","volume":"46","author":"Mahadevi","year":"2017","journal-title":"Comm. Statist. Theory Methods"},{"key":"ref_10","first-page":"149","article-title":"Estimation Methods of Alpha Power Exponential Distribution with applications to Engineering and Medical Data","volume":"16","author":"Mazen","year":"2020","journal-title":"Pak. J. Stat. Oper. Res."},{"doi-asserted-by":"crossref","unstructured":"Refah, A., Ahmed, E., Hoda, R., and Mazen, N. (2022). Inferences for Alpha Power Exponential Distribution Using Adaptive Progressively Type-II Hybrid Censored Data with Applications. 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Proceedings of the 12th Quark Confinement, Thessaloniki, Greece.","key":"ref_13"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"e08047","DOI":"10.1016\/j.heliyon.2021.e08047","article-title":"Onyemachid \u03b1-Power transformed transformed power function distribution with applications","volume":"7","author":"Idika","year":"2021","journal-title":"Heliyon"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1093\/biomet\/39.1-2.88","article-title":"Least-squares estimation of location and scale parameters using order statistics","volume":"39","author":"Lloyd","year":"1952","journal-title":"Biometrika"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A New Look at the Statistical Model Identification","volume":"19","author":"Akaike","year":"1974","journal-title":"IEEE Trans. Automat. Contr."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1198\/tech.2009.07038","article-title":"Testing Parameters of a Gamma Distribution for Small Samples","volume":"51","author":"Bhaumik","year":"2009","journal-title":"Technometrics"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/30\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:42:02Z","timestamp":1760132522000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,26]]},"references-count":17,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["sym16010030"],"URL":"https:\/\/doi.org\/10.3390\/sym16010030","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,12,26]]}}}