Comparative Analysis of Chen-type Distributions for Modelling Nigerian Stock Market: An Evaluation of Predictive Performance and Statistical Fit

This study presents a comparative analysis of Chen-type distributions for modelling the behaviour of the All-Share Index (ASI) in Nigeria, utilizing both secondary data from the Nigerian Stock Exchange (January 2008–December 2021) and simulated datasets. The study evaluates the performance of three statistical distributions: Generalized Chen (GC), New Extended Chen (NEC), and Modified Generalized Chen (MGC) based on key model selection criteria, including Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Mean Squared Error (MSE), and Likelihood Ratio Test (LRT). Descriptive statistics of the log-transformed ASI data indicate a mean of 10.33 and a standard deviation of 0.258, with a slight positive skewness (0.51) and a kurtosis value of -0.14, suggesting a near-normal distribution with moderate dispersion. The MGC distribution consistently demonstrates superior model performance, achieving the lowest AIC, BIC, and LRT values across various dataset sizes. Notably, at a dataset size of 1000, MGC records an LRT of 201,256.7, significantly lower than GC (276,903.2) and NEC (1,198,378), reinforcing its superior fit. Additionally, the NEC distribution exhibits extreme instability, with MSE values approaching infinity, making it unsuitable for predictive modelling. The probability density function (PDF) and cumulative distribution function (CDF) visualizations further confirm that MGC effectively captures the distributional properties of ASI data, while GC shows heavy-tailed behaviour, and NEC demonstrates numerical instability. These findings establish MGC as the most appropriate distribution for modelling ASI behaviour, balancing goodness-of-fit with predictive accuracy and offering a robust statistical framework for financial market analysis in Nigeria.