LH-Moments Parameter Estimation of Weibull Distribution - Guayjarernpanishk, Pannarat; Chiangpradit, Monchaya (Emerging Science Journal, 2025)
Natural disasters such as sudden floods, storms, severe snowfall, and droughts are major problems in the world. Generally the distributions of extreme values are heavy-tailed distributions, and an important heavy-tailed distribution is the Weibull distribution, especially for non-linear behaviors. Therefore, accurately estimation of the occurrence of disasters is required to deal with such situations in a timely and efficient manner. Several methods can be used to estimate the parameters, for example, moments estimate, maximum likelihood estimate, linear of moment, and high-order L-moments. The objectives of this article are to estimate the parameters of the four-parameter Weibull distribution with weak non-linear effects (W4DN) based on the LH-moments method, and to propose a new parameter estimation formula. The proposed formula is classified into two cases based on the coefficient of the second-order term (δ): Case 1, where the coefficient is positive (δ > 0) and Case 2, where the coefficient is negative (δ < 0). In both cases, the corresponding estimation formulas are derived βr and λrp for p=1, 2, ... and r=1, 2, ..., respectively. The parameter estimations (γ ̂,α ̂,δ ̂,ϕ ̂ and κ ̂) are then optimized using the augmented Lagrangian adaptive barrier minimization algorithm. These formulas provide a practical approach for parameter estimation that is essential for forecasting extreme events in various disciplines, including hydrology, meteorology, insurance, finance, and engineering.