Simulation Study on Modified Weibull Distribution for Modelling of Investment Return

Abstract

The Weibull distribution is one of the most popular statistical models extensively applied to lifetime data analysis such as survival data, reliability data, wind speed, and recently in financial data, due to itsts flexibility to adaptably imitate different families of statistical distributions. This study proposed a modified version of the two-parameter Weibull distribution by incorporating additional parameters in the internal rate of return and insurance claims data. The objective is to examine the behaviour of investment return on the assumption of the proposed model. The proposed and the existing Weibull distribution parameters have been estimated via a simulated annealing algorithm. Experimental simulations have been conducted mimicking the internal rate of return (IRR) data for both short time (small sample) and long-term investment periods (large samples). The performance of the proposed model has been compared with the existing two-parameter Weibull distribution model in terms of their R-square (R2), mean absolute error (MAE), root mean squared error (RMSE), Akaike’s information criterion (AIC), and the Kolmogorov-Smirnov test (KS). The numerical simulation revealed that the proposed model outperformed the existing two-parameter Weibull distribution model in terms of accuracy, robustness, and sensitivity. Therefore, it can be concluded that the proposed model is entirely suitable for the long-term investment period. The study will be extended using the internal rate of return real data set. Furthermore, a comparison of the various Weibull distribution parameter estimators such as metaheuristics or evolutionary algorithms based on the proposed model will be carried out.