In this article, we define a new family of models, called the beta Marshall-Olkin extended log-logistic family of distributions (BMO-LL), by adding three shape parameters that generalize some well-known distributions in statistics, such as the log-logistic distribution. We obtain estimates of the model parameters using the methods of moments, maximum likelihood, and Bayesian. Finally, we fit some specific models in the new family to a real datasets to demonstrate their flexibility in fitting to the life data. It is found that the BMO-LL model fits better than competing models, so it can be considered as a suitable distribution for fitting to the life data.
