A novel four-parameter log-logistic model: mathematical properties and applications to breaking stress, survival times and leukemia data

In this paper, we introduce a new continuous log-logistic extension. Several of its properties are established. A numerical analysis for skewness and kurtosis is presented. The new failure rate can be "bathtub or U shaped", "increasing", "decreasing-constant", "J shaped", "constant" and "decreasing". Many bivariate and Multivariate type distributions are derived using the Clayton Copula and the Morgenstern family. To assess of the finite sample behavior of the estimators, we performed a graphical simulation. Some useful applications are considered for supporting the new model.