New Generalized and Dual Generalized Order Statistics based Transmuted Log-Logistic Distributions

This paper introduces two extensions of the log-logistic distribution, namely the generalized order statistics transmuted log-logistic (GOSTLL) and the dual generalized order statistics transmuted log-logistic (DGOSTLL) distributions. These models are constructed based on the generalized and dual generalized order statistics based transmuted families of distributions. Some important statistical properties including reliability measures, hazard rate functions, entropies, etc. are studied. The maximum likelihood estimation of the parameters is presented for both of the new distributions. The usefulness of the proposed distributions is demonstrated through real data applications.