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.

Generalized gamma distribution based on the Bayesian approach with application to investment modelling

“…This study focused on the Markov Chain Monte-Carlo (MCMC)-based Bayesian estimation of the Generalized Gamma Distribution (GGD) utilizing the Adaptive Rejection Metropolis Sampling (ARMS) technique of random variable generation within the Gibbs sampler algorithm based on two case studies involving simulated data from [14,37,38] and actual data of Modified Internal Rate of Return (MIRR) from [37][38][39]. The results of applying the ARMS method are compared with those of the application of the SA algorithm in the case of simulated data and with those of the Method of Moment (MM) and SA applications for the real MIRR data.…”

“…Some of the parameter estimation methods include the Least Squares (LS) estimation of GGD parameters presented in [12,13]. An alternative method of estimation for GGD parameters based on heuristic optimization approaches was proposed [14,15]. The heuristics approach was found to be effective.…”

Tractor Rollover Accidents: A Review of Factors and Safety Measures

“…Even in cases of minor damage, valuable time is lost in repairing and restoring the tractor's functionality. While safety cabs have been installed in most agricultural tractors, reducing the risk of death or injury, the underlying causes of tractor overturning persist due to factors like the high center of gravity and the frequent use of tractors on sloping or uneven terrain [5][6][7][8].…”

A Bayesian Framework for Estimating Weibull Distribution Parameters: Applications in Finance, Insurance, and Natural Disaster Analysis

“…In the realm of statistical distributions, which describe the probabilistic behavior of random phenomena, researchers have devoted considerable attention to various distributions, such as the normal distribution, Pareto distribution, gamma distribution, Maxwell distributions, and Poisson distribution (Carrasco et al, 2008;Cordeiro et al, 2014;De Pascoa et al, 2011;Emmert-Streib & Dehmer, 2019;Jazi et al, 2010). These distributions have proven their usefulness in different domains, including science, engineering, business, and finance (Abubakar & Muhammad Sabri, 2021;Abubakar & Sabri, 2022Jiang, 2020;Kobayashi et al, 2011;Yu, 2022).…”