{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T06:08:20Z","timestamp":1770962900001,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T00:00:00Z","timestamp":1769817600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The natural generalization of the XLindley distribution is proposed. The mathematical properties of the generalized XLindley distribution are derived. The importance of the proposed model is evaluated on the first-order autoregressive process, and compared with its counterparts. Extensive simulation studies are carried out to demonstrate the suitability of the estimation methods. Empirical findings reveal that the first-order autoregressive process with generalized XLindley innovations produces better forecasting results than those of the gamma, weighted Lindley, and normal innovations. Additionally, a web-tool application of the proposed model is developed and deployed on a free server that is accessible for practitioners.<\/jats:p>","DOI":"10.3390\/axioms15020107","type":"journal-article","created":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T09:00:33Z","timestamp":1770022833000},"page":"107","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Natural Generalization of the XLindley Distribution and Its First-Order Autoregressive Process with Applications to Non-Gaussian Time Series"],"prefix":"10.3390","volume":"15","author":[{"given":"Emrah","family":"Altun","sequence":"first","affiliation":[{"name":"Department of Statistics, Gazi University, Ankara 06560, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Soheyla A.","family":"Ghomeishi","sequence":"additional","affiliation":[{"name":"Department of Statistics, Gazi University, Ankara 06560, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7577-6079","authenticated-orcid":false,"given":"Hana N.","family":"Alqifari","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, Qassim University, Buraydah 52571, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.1080\/03610928808829693","article-title":"On AR (1) processes with exponential white noise","volume":"17","author":"Andel","year":"1988","journal-title":"Commun. 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Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"e2724","DOI":"10.1002\/env.2724","article-title":"A notable Gamma-Lindley first-order autoregressive process: An application to hydrological data","volume":"33","author":"Mello","year":"2022","journal-title":"Environmetrics"},{"key":"ref_6","first-page":"31","article-title":"On autoregressive processes with Lindley-distributed innovations: Modeling and simulation","volume":"25","author":"Nitha","year":"2024","journal-title":"Stat. Transit."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4988","DOI":"10.1080\/03610926.2014.935429","article-title":"Lindley first-order autoregressive model with applications","volume":"45","author":"Bakouch","year":"2016","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.56947\/amcs.v29.573","article-title":"A first-order autoregressive process with weighted Lindley innovations and its applications to energy and financial data","volume":"29","author":"Gabr","year":"2025","journal-title":"Ann. Math. Comput. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1177\/0008068317732196","article-title":"A Bayesian approach to robust skewed autoregressive processes","volume":"69","author":"Maleki","year":"2017","journal-title":"Calcutta Stat. Assoc. Bull."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1761","DOI":"10.1016\/j.jmva.2009.02.006","article-title":"Estimation of autoregressive models with epsilon-skew-normal innovations","volume":"100","author":"Bondon","year":"2009","journal-title":"J. Multivar. Anal."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"318","DOI":"10.2991\/jsta.d.210607.001","article-title":"The XLindley distribution: Properties and application","volume":"20","author":"Chouia","year":"2021","journal-title":"J. Stat. Theory Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1007\/s40995-017-0237-6","article-title":"Autoregressive models with mixture of scale mixtures of Gaussian innovations","volume":"41","author":"Maleki","year":"2017","journal-title":"Iran. J. Sci. Technol. Trans. A Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3393","DOI":"10.1080\/03610926.2015.1060347","article-title":"On the estimation of missing values in AR (1) model with exponential innovations","volume":"46","author":"Saadatmand","year":"2017","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1016\/j.matcom.2007.06.007","article-title":"Lindley distribution and its application","volume":"78","author":"Ghitany","year":"2008","journal-title":"Math. Comput. Simul."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"38","DOI":"10.22237\/jmasm\/1462077420","article-title":"The xgamma distribution: Statistical properties and application","volume":"15","author":"Sen","year":"2016","journal-title":"J. Mod. Appl. Stat. Methods"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"20180018","DOI":"10.1515\/jtse-2018-0018","article-title":"Checking model adequacy for count time series by using Pearson residuals","volume":"12","author":"Scherer","year":"2020","journal-title":"J. Time Series Econom."},{"key":"ref_17","first-page":"105","article-title":"Gaussian estimation in stationary time series","volume":"39","author":"Whittle","year":"1961","journal-title":"Bull. Int. Stat. Inst."},{"key":"ref_18","unstructured":"Chang, W., and Borges Ribeiro, B. (2025, November 15). shinydashboard: Create Dashboards with \u2019Shiny\u2019. R Package Version 0.7.2. Available online: https:\/\/CRAN.R-project.org\/package=shinydashboard."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wickham, H. (2016). ggplot2: Elegant Graphics for Data Analysis, Springer.","DOI":"10.1007\/978-3-319-24277-4_9"},{"key":"ref_20","unstructured":"Qiu, D. (2025, November 15). aTSA: Alternative Time Series Analysis. R Package Version 3.1.2.1. Available online: https:\/\/CRAN.R-project.org\/package=aTSA."},{"key":"ref_21","unstructured":"Hamner, B., and Frasco, M. (2025, November 15). Metrics: Evaluation Metrics for Machine Learning. R Package Version 0.1.4. Available online: https:\/\/CRAN.R-project.org\/package=Metrics."},{"key":"ref_22","unstructured":"Gilbert, P., and Varadhan, R. (2025, November 15). numDeriv: Accurate Numerical Derivatives. R Package Version 2016.8-1.1. Available online: https:\/\/CRAN.R-project.org\/package=numDeriv."},{"key":"ref_23","unstructured":"Evert, S., and Baroni, M. (2007, January 23\u201330). zipfR: Word frequency distributions in R. Proceedings of the 45th Annual Meeting of the Association for Computational Linguistics, Posters and Demonstrations Sessions, Prague, Czech Republic."},{"key":"ref_24","unstructured":"Xie, Y., Cheng, J., and Tan, X. (2025, November 15). DT: A Wrapper of the JavaScript Library \u2019DataTables\u2019. R Package Version 0.33. Available online: https:\/\/CRAN.R-project.org\/package=DT."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/15\/2\/107\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T05:14:48Z","timestamp":1770959688000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/15\/2\/107"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,31]]},"references-count":24,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,2]]}},"alternative-id":["axioms15020107"],"URL":"https:\/\/doi.org\/10.3390\/axioms15020107","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,31]]}}}