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Several mathematical properties of the new modified-$ G $ family are derived. Based on the new modified-$ G $ method, a new updated version of the Weibull model called, a new modified-Weibull distribution is introduced. Furthermore, the estimators of the parameters of the new modified-$ G $ distributions are also obtained. Finally, the applicability of the new modified-Weibull distribution is illustrated by analyzing two medical sets. Using certain analytical tools, it is observed that the new modified-Weibull distribution is the best choice to deal with the medical data sets.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/mbe.2022490","type":"journal-article","created":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T10:36:00Z","timestamp":1658745360000},"page":"10474-10492","source":"Crossref","is-referenced-by-count":7,"title":["A new statistical approach for modeling the bladder cancer and leukemia patients data sets: Case studies in the medical sector"],"prefix":"10.3934","volume":"19","author":[{"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":"Zubair","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Statistics, Yazd University, P.O. Box 89175-741, Yazd, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elsayed","family":"tag-Eldin","sequence":"additional","affiliation":[{"name":"Faculty of Engineering and Technology, Future University in Egypt New Cairo 11835, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zahra","family":"Almaspoor","sequence":"additional","affiliation":[{"name":"Department of Statistics, Yazd University, P.O. Box 89175-741, Yazd, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed S.","family":"Eliwa","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operation Research, College of Science, Qassim University, P.O. Box 6644, Buraydah 51482, Saudi Arabia"},{"name":"Department of Statistics and Computer Science, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zahoor","family":"Iqbal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2321","reference":[{"key":"key-10.3934\/mbe.2022490-1","doi-asserted-by":"publisher","unstructured":"M. El-Morshedy, M. S. Eliwa, The odd flexible Weibull-H family of distributions: Properties and estimation with applications to complete and upper record data, <i>Filomat<\/i>, <b>33<\/b> (2019), 2635\u20132652. https:\/\/doi.org\/10.2298\/FIL1909635E","DOI":"10.2298\/FIL1909635E"},{"key":"key-10.3934\/mbe.2022490-2","doi-asserted-by":"publisher","unstructured":"C. B. de Villiers, M. Kroese, S. 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