Bhatti, Fiaz AhmadHamedani G.G.Korkmaz, Mustafa ÇağatayCordeiro, Gauss M.Yousof, Haitham M.Ahmad, Munir2025-07-092025-07-09201921955832https://hdl.handle.net/11494/5698In this paper, a flexible family of distributions with unimodel, bimodal, increasing, increasing and decreasing, inverted bathtub and modified bathtub hazard rate called Burr III-Marshal Olkin-G (BIIIMO-G) family is developed on the basis of the T-X family technique. The density function of the BIIIMO-G family is arc, exponential, left- skewed, right-skewed and symmetrical shaped. Descriptive measures such as quantiles, moments, incomplete moments, inequality measures and reliability measures are theoretically established. The BIIIMO-G family is characterized via different techniques. Parameters of the BIIIMO-G family are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of BIIIMO-G family is demonstrated by its application to real data sets.eninfo:eu-repo/semantics/openAccessCharacterizationsMaximum likelihood estimationMomentsReliabilityArticle6110.1186/s40488-019-0101-72-s2.0-85071241305