Different Classical and Bayesian Methods of Estimation of the Power Log-Logistic Distribution with Applications

A new approach in constructing a univariate absolutely continuous probability model via power transformation is adopted. The proposed distribution appears to subsume several popular univariate continuous probability models that are already existent in the literature. In addition, the hazard rate function of the proposed distribution appears to possess all possible shapes, increasing, decreasing, and upside-down which is not present in all existing extensions and generalizations of the log-logistic (LL) distribution. Various established estimation strategies under the classical approach such as maximum product spacing, weighted least squares estimation, etc., are adopted to exhibit the flexibility of the proposed probability distribution. The emphasis has been made on the estimation procedure and the new probability model is indeed augmenting the existing literature in many aspects which are highlighted in the simulation and also in the real data application section.