{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:21:03Z","timestamp":1760239263985,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,10,14]],"date-time":"2020-10-14T00:00:00Z","timestamp":1602633600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"strategic technology program of the National Plan for Science, Technology and Innovation in the Kingdom of Saudi Arabia","award":["14-MAT2052-02"],"award-info":[{"award-number":["14-MAT2052-02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A new method for generalizing the Lindley distribution, by increasing the number of mixed models is presented formally. This generalized model, which is called the generalized Lindley of integer order, encompasses the exponential and the usual Lindley distributions as special cases when the order of the model is fixed to be one and two, respectively. The moments, the variance, the moment generating function, and the failure rate function of the initiated model are extracted. Estimation of the underlying parameters by the moment and the maximum likelihood methods are acquired. The maximum likelihood estimation for the right censored data has also been discussed. In a simulation running for various orders and censoring rates, efficiency of the maximum likelihood estimator has been explored. The introduced model has ultimately been fitted to two real data sets to emphasize its application.<\/jats:p>","DOI":"10.3390\/sym12101678","type":"journal-article","created":{"date-parts":[[2020,10,17]],"date-time":"2020-10-17T07:23:22Z","timestamp":1602919402000},"page":"1678","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A New Flexible Generalized Lindley Model: Properties, Estimation and Applications"],"prefix":"10.3390","volume":"12","author":[{"given":"Abdulrahman","family":"Abouammoh","sequence":"first","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6363-1246","authenticated-orcid":false,"given":"Mohamed","family":"Kayid","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia"},{"name":"Department of Mathematics and Computer Science, Faculty of Science, Suez University, Suez 43511, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1111\/j.2517-6161.1958.tb00278.x","article-title":"Fiducial distributions and Bayes\u2019 theorem","volume":"20","author":"Lindley","year":"1958","journal-title":"J. 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