Advancing Statistical Modelling: A Comparative Study of Zero-Truncated Distributions in Economic Analysis

Abstract

This study explores the application of two zero-truncated distributions, Geometric-Zero Truncated Poisson (GZTP) and Zero-Truncated Poisson Pareto (ZTPP), in modelling economic datasets, with a particular focus on Nigeria’s key economic indicators. Secondary data from the Central Bank of Nigeria’s Statistical Bulletin (2021), spanning from 1989 to 2020, was used, covering variables such as Real Gross Domestic Product (RGDP), export and import goods, money supply, and Brent crude oil prices. The objectives were to: Introduce and describe the mathematical properties of the GZTP and ZTPP distributions; compare the performance of these distributions across datasets using metrics such as AIC, BIC, and MSE; and recommend the most efficient distribution for modelling economic variables and predicting trends. The study employs the Maximum Likelihood Estimation (MLE) method for parameter estimation, implemented in R programming. Model performance was evaluated using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Mean Squared Error (MSE). The results indicate that the ZTPP distribution outperforms the GZTP distribution across all datasets, with significantly lower AIC, BIC, and MSE values. Specifically, the ZTPP achieved an average AIC of -1422.54, BIC of -1422.55, and MSE of 30,161.94, compared to the GZTP’s -766.39, -762.82, and 31,163.2, respectively. These findings highlight the superior model fit and predictive accuracy of the ZTPP distribution, making it a more robust tool for economic analysis, particularly in cases where zero occurrences are impossible. This comparative study underscores the importance of choosing the right distribution for economic modelling to achieve high accuracy and reliable results.