The Odd Ramos-Louzada Generator of distributions with applications to failure and waiting times

Abstract

In this study, we have proposed a new generator called the Odd Ramos-Louzada Generator (ORL-G), which can extend many well-known distributions by applying the T-X method. Some of its basic statistical properties such as the quantile function, the rthnon-central moments and Renyi entropy are also investigated. The ORL-G has the ability to model symmetric and asymmetric data as well as non-monotonic and monotonic failure rate datasets. Three new distributions of the ORL-G family are the ORL-Burr XII (ORLBXII), ORL-Log Logistic (ORLLoL), and ORL-Weibull (ORLWei) which are respectively obtained using the Burr XII, the Log-Logistic, and Weibull as baseline models. The RL and Generalized RL distributions are sub-models of the ORLBXII and ORLLoL distributions. The ORL-G model parameters have been estimated using the maximum likelihood (ML) method. Simulation analysis carried out indicates that the ML estimation method and its asymptotic properties performed quite well. The flexibility of the ORL-G family is demonstrated through the application of three real, complete datasets, including failure and waiting times and it is evident that ORLBXII outperformed its sub-models and other competing models.

Keywords

• Ramos-Louzada
• Generator
• T-X family
• Statistical properties
• ML estimation
• Simulation