Simulation analysis, properties and applications on a new Burr XII model based on the Bell-X functionalities

<abstract><p>In this article, we make mathematical and practical contributions to the Bell-X family of absolutely continuous distributions. As a main member family, special distribution extending modeling perspectives famous Burr XII (BXII) is discussed in detail. It called Bell-Burr (BBXII) distribution. stands apart from other extended BXII distributions because its flexibility terms functional shapes. On theoretical side, linear representation probability density function ordinary incomplete moments are among key properties studied depth. Some commonly used entropy measures, namely Rényi, Havrda Charvat, Arimoto, Tsallis entropy, derived. (inferential) associated parameters estimated using seven different frequentist estimation methods, methods maximum likelihood estimation, percentile least squares weighted Cramér von-Mises Anderson-Darling right-tail estimation. A simulation study utilizing all these offered highlight their effectiveness. Subsequently, BBXII model successfully comparisons with comparable models analyze data on patients acute bone cancer arthritis pain. group acceptance sampling plan for truncated life tests also proposed when an item's lifetime follows Convincing results obtained.</p></abstract>