Efficient Entropy Estimation Genetic Algorithm – Random Forest Optimization for inverted Weibull Pareto distribution using Fuzzy Ranked set Sampling: A comparative Study

Abstract

Entropy-based measures, give a principled measure of uncertainty and information content in lifetime and reliability models. The research formulates and contrasts estimators of four generalized entropies (Renyi, Tsallis, Havard Charvat and Arimoto) of the proposed inverted Weibull-Pareto (IWP) distribution, a flexible heavy-tailed distribution derived by a multiplicative Weibull-Pareto survival mechanism with an additive hazard structure. Estimation is done assuming simple random sampling (SRS) and ranked set sampling (RSS) with perfect and imperfect ranking. Along with the classical methods, including maximum likelihood, maximum product spacing, Kolmogorov-based, least squares, weighted least squares, Anderson-Darling, and Cramer-Mises, we propose an informed nested genetic algorithm based-random forest (GA-RF) method to enhance numerical stability and predictive power. The proposed a fuzzy Monte Carlo simulation framework to include epistemic uncertainty in model parameters and ranking quality through 8 -cut representations and performance is evaluated in terms of absolute bias, mean squared error, and relative efficiency given equal measurement effort. In all the simulation situations, RSS has better estimation accuracy compared to SRS and perfect ranking is better than imperfect ranking. The tensile-strength (GPa) data of 79 carbon fibres provided by Bader and Priest is used as an example of the methodology, which indicates that the GARF method, with RSS, provides the best goodness-of-fit diagnostics, which proves the practical benefits of information-enriched sampling and smart estimation of entropy.