Properties and estimation approaches of the odd JCA family with applications

Summary In this article, we study a new generator of distributions called the odd JCA‐G family. We determine the main mathematical properties of the new family. Some special submodels of the odd JCA‐G family are presented. The special models of the JCA‐G family have tractable densities shapes which possess various kinds of asymmetric, reversed‐J, left‐skewed, right‐skewed, symmetrical shapes. Furthermore, special submodels exhibit flexible hazard rate shapes. Additionally, the parameters of the odd JCA Burr‐XII model are estimated using some classical estimation approaches. The performance and efficiency of these approaches are explored via numerical simulations. The applicability of the odd JCA‐G family is illustrated by fitting two real‐life datasets. The data analysis shows that the odd JCA Burr‐XII model outperforms some well‐known distributions for the selected data.