{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T04:31:06Z","timestamp":1782880266846,"version":"3.54.5"},"reference-count":29,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T00:00:00Z","timestamp":1699920000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University","award":["PNURSP2023R 299"],"award-info":[{"award-number":["PNURSP2023R 299"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>It is proven evidently that probability distributions have a significant role in data modeling for decision-making. Due to the indispensable role of probability distributions for data modeling in applied fields, a series of probability distributions have been introduced and implemented. However, most newly developed probability distributions involve between one and eight additional parameters. Sometimes the additional parameters lead to re-parametrization problems. Therefore, the development of new probability distributions without additional parameters is an interesting research topic. In this paper, we study a new probabilistic method without incorporating any additional parameters. The proposed approach is based on a tangent function and may be called a new tangent-G (NT-G) family of distributions. Certain properties of the NT-G distributions are derived. Based on the NT-G method, a new flexible probability distribution called a new tangent flexible Weibull (NTF-Weibull) distribution is studied. The parameters of the NTF-Weibull distribution are estimated using seven different estimation methods. Based on these eight estimations, a brief simulation of the NTF-Weibull distribution is also provided. Finally, we prove the applicability of the NTF-Weibull distribution by analyzing two waiting-time data sets taken from the reliability sector. We consider three statistical tests with a p-value to evaluate the performance and goodness of fit of the NTF-Weibull distribution.<\/jats:p>","DOI":"10.3390\/sym15112066","type":"journal-article","created":{"date-parts":[[2023,11,15]],"date-time":"2023-11-15T00:47:48Z","timestamp":1700009268000},"page":"2066","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A New Tangent-Generated Probabilistic Approach with Symmetrical and Asymmetrical Natures: Monte Carlo Simulation with Reliability Applications"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5154-7477","authenticated-orcid":false,"given":"Huda M.","family":"Alshanbari","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3430-2464","authenticated-orcid":false,"given":"Hazem","family":"Al-Mofleh","sequence":"additional","affiliation":[{"name":"Division of Science and Mathematics, Eureka College, Eureka, IL 61530, USA"},{"name":"Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-4811-4138","authenticated-orcid":false,"given":"Jin-Taek","family":"Seong","sequence":"additional","affiliation":[{"name":"Graduate School of Data Science, Chonnam National University, Gwangju 61186, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Saima K.","family":"Khosa","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, SK S7N 5A2, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Jimichi, M., Kawasaki, Y., Miyamoto, D., Saka, C., and Nagata, S. 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