Optimization of Weibull Distribution Parameters with Application to Short-Term Risk Assessment and Strategic Investment Decision-Making

Abstract

Accurate parameter estimation is fundamental in financial modeling, especially in investment analysis, where the Modified Internal Rate of Return (MIRR) plays a key role in evaluating investment performance. This study aims to enhance risk and return predictions in Sharia-compliant property investments by exploring the efficacy of various optimization techniques for estimating Weibull distribution parameters within the MIRR framework. To achieve this, we employed a comparative analysis of optimization methods, including Simulated Annealing (SA), Differential Evolution (DE), Genetic Algorithm (GA), and traditional Numerical Methods (NM). Performance was assessed through metrics such as Root Mean Squared Error (RMSE), Akaike Information Criterion (AIC), R-squared (R2) values, and Kolmogorov-Smirnov (KS) statistics. The results reveal that metaheuristic algorithms (SA, DE, GA) significantly outperform traditional numerical methods in terms of parameter estimation accuracy. Specifically, SA achieved the lowest RMSE of 0.042, with a Weibull shape parameter estimate of 1.254 and variance of 0.004, followed closely by DE with an RMSE of 0.048, and GA with 0.046. In contrast, NM exhibited a higher RMSE of 0.067, with a shape parameter estimate of 1.310 and a variance of 0.006. The AIC values for metaheuristic methods ranged from 14.25 to 14.68, compared to 15.12 for NM, and R2 values for metaheuristic methods ranged from 0.932 to 0.945, compared to 0.910 for NM. KS statistics further underscored the superior model fit of metaheuristics, with SA showing the lowest KS value of 0.045. The study underscores the critical role of metaheuristic optimization in improving the accuracy of parameter estimation based on MIRR models. This enhancement provides more reliable risk assessments and returns predictions, offering valuable insights for informed investment decision-making and contributing to optimized financial outcomes in the property sector.