Statistical Modelling of Nigeria’s Gross Fixed Capital Formation Using Fréchet-based Distributions

This study employed a quantitative research design to statistically model Nigeria’s Gross Fixed Capital Formation (NGFCF) using Fréchet-based distributions, assessing its distributional properties and economic implications. A secondary dataset from 1981 to 2020 was sourced from the Central Bank of Nigeria’s Statistical Bulletin and the World Bank national accounts data. The research approach involves both empirical analysis and simulation techniques to examine NGFCF's statistical behaviour. A log transformation was applied to NGFCF to stabilize variance and improve normality, which was tested using the Anderson-Darling (AD) test statistic. Four Fréchet-based distributions Kumaraswamy Fréchet (KF), Exponentiated Fréchet (EF), Beta Fréchet (BF), and standard Fréchet (F) were considered for modelling NGFCF. The Maximum Likelihood Estimation (MLE) method was employed for parameter estimation, and model performance was evaluated using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Likelihood Ratio Test (LRT). Simulated sample sizes were analyzed to assess model robustness. The Exponentiated Fréchet distribution exhibited the best fit, as evidenced by the lowest AIC and BIC values and the highest LRT statistics, making it the most suitable model for capturing the heavy-tailed nature of NGFCF. These findings highlight the role of flexible statistical models in economic forecasting and risk assessment, providing a refined approach to understanding Nigeria’s capital formation patterns.