This study introduces a new generalized family of continuous probability distributions, termed the Odd Lomax-G (OLG) family. A special three-parameter model, the Odd Lomax-G Exponential (OLE) distribution, is also proposed as a member of this family. The derivation of the new family is based on binomial series expansion, logarithmic, and exponential transformations, which expand the flexibility and applicability of existing distributions.
The paper presents detailed mathematical properties of the proposed models, including the moment generating function (mgf), quantity function, ordered statistics, and Rényi entropy. Parameter estimation is carried out using the Maximum Likelihood Estimation (MLE) method, and the performance of the estimators is evaluated through two real-life data applications.
Results demonstrate the superior goodness of fit and flexibility of the new OLG family and its sub-models, particularly the OLE distribution, in modeling diverse datasets.