The Extended Log-Logistic Distribution: Inference and Actuarial Applications

Actuaries are interested in modeling actuarial data using loss models that can be adopted to describe risk exposure. This paper introduces a new flexible extension of the log-logistic distribution, called extended (Ex-LL) model heavy-tailed insurance losses data. The Ex-LL hazard function exhibits an upside-down bathtub shape, increasing J decreasing and reversed-J shape. We derived five important measures based on distribution. parameters were estimated different estimation methods, their performances assessed simulation results. Finally, performance distribution was explored two types real from engineering sciences. analyzed illustrated provided adequate fit compared other competing distributions such as log-logistic, alpha-power transmuted generalized Marshall–Olkin inverse Weibull distributions.