On Estimating the Parameters of the Generalised Gamma Distribution based on the Modified Internal Rate of Return for Long-Term Investment Strategy

Abstract

The generalised gamma distribution (GGD) is one of the most widely used statistical distributions used extensively in several scientific and engineering application areas due to its high adaptability with the normal and exponential, lognormal distributions, among others. However, the estimation of the unknown parameters of the model is a challenging task. Many algorithms were developed for parameter estimation, but none can find the best solution. In this study, a simulated annealing (SA) algorithm is proposed for the assessment of effectiveness in determining the parameters for the GDD using modified internal rate of return (MIRR) data extracted from the financial report of the publicly traded Malaysian property companies for long term investment periods (2010–2019). The performance of the SA is compared to the moment method (MM) based on mean absolute error (MAE) and root mean squares errors (RMSE) based on the MIRR data set. The performance of this study reveals that the SA algorithm has a better estimate with the increases in sample size (long-term investment periods) compared to MM, which reveals a better estimate with a small sample size (short-time investment periods). The results show that the SA algorithm approach provides better estimates for GGD parameters based on the MIRR data set for the long-term investment period.