{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T15:29:50Z","timestamp":1772033390659,"version":"3.50.1"},"reference-count":18,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,16]],"date-time":"2022-12-16T00:00:00Z","timestamp":1671148800000},"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 importance of counting data modeling and its applications to real-world phenomena has been highlighted in several research studies. The present study focuses on a one-parameter discrete distribution that can be derived via the survival discretization approach. The proposed model has explicit forms for its statistical properties. It can be applied to discuss asymmetric \u201cright skewed\u201d data with long \u201cheavy\u201d tails. Its failure rate function can be used to discuss the phenomena with a monotonically decreasing or unimodal failure rate shape. Further, it can be utilized as a probability tool to model and discuss over- and under-dispersed data. Various estimation techniques are reported and discussed in detail. A simulation study is performed to test the property of the estimator. Finally, three real data sets are analyzed to prove the notability of the introduced model.<\/jats:p>","DOI":"10.3390\/axioms11120737","type":"journal-article","created":{"date-parts":[[2022,12,19]],"date-time":"2022-12-19T08:41:41Z","timestamp":1671439301000},"page":"737","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Discrete Single-Factor Extension of the Exponential Distribution: Features and Modeling"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7585-5519","authenticated-orcid":false,"given":"Mahmoud","family":"El-Morshedy","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hend S.","family":"Shahen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bader","family":"Almohaimeed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51482, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5619-210X","authenticated-orcid":false,"given":"Mohamed S.","family":"Eliwa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"},{"name":"Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia"},{"name":"Department of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bhatti, F.A., Hamedani, G.G., Korkmaz, M.\u00c7., Sheng, W., and Ali, A. 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