On Empirical Selection of Lognormal and Weibull Distributions: Application to Nigerian Stock Market

In this article, we empirically compared and selected the best performed distribution among Lognormal and Weibull distributions. The dataset for this study were monthly stock prices of BUA cement enlisted and trades on Lagos Stock Exchange, a subsidiary of Nigeria Stock Exchange (NSE). The dataset comprised of sample of fifty-eight (58) log-transformed monthly closed stock prices between 2nd January, 2020 and 1st November, 2024, obtained from https://ng.investing.com/equities/bua-cement-plc-historical-data .The Maximum Likelihood Estimator (MLE) was used to obtain the parameters of both Lognormal and Weibull distributions in a view of comparing and selecting the best distribution that fits our dataset. The Minimum Mean Squared Error (MSE) and Akaike Information Criterion (AIC) were used as selection criteria and the Weibull distribution was found to outperform the Lognormal distribution since it exhibited the least MSE and AIC. Also, the selected Weibull distribution was subjected to goodness-of-fit using Kolmogorov-Smirnov test and the empirical evience shows that BUACEM stock price follows a Weibull distribution with 5% level of significance, hence, making the Weibull distribution the right choice for fitting BUACEM stock prices on the Nigerian Stock market.