Improved Shape Parameter Estimation for the Three-Parameter Log-Logistic Distribution

The log-logistic distribution is widely used in different fields of study such as survival analysis, hydrology, insurance, and economics. Recently, Ahsanullah Alzaatreh studied the best linear unbiased estimators for location scale parameters three-parameter model. same authors also propose a shift-invariant Hill estimator unknown shape parameter. In this work, we new estimation method We derive its nondegenerate asymptotic behaviour analyse finite sample performance through Monte Carlo simulation study. To have precise estimates, present selecting threshold. illustrate improvement achieved, efficiency comparisons are provided.