New modified light tail Weibull distribution with application to automobile collision data and PORT-VaR analysis

Heavy and light-tailed distributions are crucial for modeling extreme values in actuarial science, finance, and reliability. This paper proposes a modified light-tailed Weibull distribution, incorporating an additional shape parameter to better capture varying tail behaviors. We investigate some fundamental statistical properties and risk measures. Parameters are estimated using seven methods including Maximum Likelihood, Maximum Product of Spacing, Anderson-Darling, Cramér-von Mises, Least-Squares, Weighted Least-Squares, and Percentile methods and their performance compared via Monte Carlo simulations. Fitting the model to automobile collision data demonstrates its superior fit and flexibility over competing distributions. Finally, a peaks-over-random-threshold VaR analysis is conducted on the insurance data.