A New Extending Inverse Weibull Distribution to Handle Neutrosophic Logic: Mathematical Properties, Parameters Estimation, and Simulation with Application

The study aims to present a new extinction of the inverse Weibull distribution within the modified Weibull (MWG) family to address uncertainty in neutrosophic logic , called Neutrosophic Modified Weibull Inverse Weibull (NMWIW) distribution . The mathematical properties of the proposed distribution , including its density , distribution , and survival functions , were analyzed , with parameter estimation using three method (MLE ,LSE and WLSE ) . Monte Carlo simulation demonstrated the superiority of the MLE method in terms of estimation accuracy to the MSE ,RMSE and BIAs criteria. The model was applied to two datasets : the daily COVED-19 death rate in the Netherlands (March 31 – April 30 , 2020) and estimated under five mortality periods. The result demonstrated the superiority of the NMWIW compared to six other distribution (e.g., NBIW , NKIW) using information criteria (AIC,BIC) and statistical measures (K-S , p-value), proving its effectiveness in modeling real-world data uncertain conditions. The graphs also confirmed the model's fit to the experimental data, making it a powerful tool for risk analysis and decision making under ambiguous data.