Generalization of Odd Ramos-Louzada generated family of distributions: Properties, characterizations, and applications to diabetes and cancer survival datasets

Probability distributions offer the best description of survival data and as a result, various lifetime models have been proposed. However, some of these survival datasets are not followed or sufficiently fitted by the existing proposed probability distributions. This paper presents a novel Kumaraswamy Odd Ramos-Louzada-G (KumORL-G) family of distributions together with its statistical features, including the quantile function, moments, probability-weighted moments, order statistics, and entropy measures. Some relevant characterizations were obtained using the hazard rate function and the ratio of two truncated moments. In light of the proposed KumORL-G family, a five-parameter sub-model, the Kumaraswamy Odd Ramos-Louzada Burr XII (KumORLBXII) distribution was introduced and its parameters were determined with the maximum likelihood estimation (MLE) technique. Monte Carlo simulation was performed and the numerical results were used to evaluate the MLE technique. The proposed probability distribution's significance and applicability were empirically demonstrated using various complete and censored datasets on the survival times of cancer and diabetes patients. The analytical results showed that the KumORLBXII distribution performed well in practice in comparison to its sub-models and several other competing distributions. The new KumORL-G for diabetes and cancer survival data is found extremely efficient and offers an enhanced and novel technique for modeling survival datasets.