Evaluating the Performance of Laplace and Its Variants in Modelling Economic Data.

Abstract:

The Laplace distribution and its extensions have been widely utilized in statistical modelling due to their ability to capture real-world data characteristics such as skewness and heavy tails. This study evaluates the performance of the classical Laplace (L) distribution against three of its variants: the Transmuted Laplace (TL), Alternative Laplace (AL), and Asymmetric Laplace (ASL) distributions. While these extensions introduce additional parameters to enhance flexibility, their empirical performance remains a subject of interest. Using three datasets Rent prices, Voltage Drop, and Nigeria’s Unemployment Rate. This study assesses model fit based on the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Mean Squared Error (MSE). Findings reveal that the standard Laplace (L) distribution consistently outperforms its counterparts. In the Rent dataset, it achieves the lowest AIC (613.636), BIC (609.2266), and a reasonable MSE (2343.761), whereas the TL and AL distributions yield significantly higher AIC and BIC values, and the ASL distribution demonstrates an extremely high MSE (9.34 × 10¹²), indicating poor fit. A similar trend is observed in the Voltage Drop dataset, where the L distribution records the lowest AIC (201.1564), BIC (197.7293), and MSE (132.7978), while TL and ASL show excessive model instability. In the Unemployment Rate dataset, the L distribution again provides the best fit, with an AIC of 349.7985, a BIC of 345.896, and a moderate MSE of 186.4666. On average, across all datasets, the L distribution remains the most robust model, with the lowest AIC (388.197), BIC (384.284), and MSE (887.6751). The AL distribution follows closely with an MSE of 888.9518 but exhibits significantly higher AIC (2426.027) and BIC (2424.071). The ASL distribution, while demonstrating moderate AIC (1443.016) and BIC (1448.885), suffers from poor predictive accuracy with an extremely high MSE (3.19E+12). The TL distribution performs the worst, with the highest AIC (34,686.77), BIC (20,112.08), and an MSE of 76,038.22, highlighting its instability. In conclusion, this study establishes that the standard Laplace (L) distribution provides the most reliable and accurate fit across diverse datasets. While alternative forms introduce additional flexibility, their increased complexity does not necessarily yield superior model performance. Future research should explore modifications to improve the parameter stability of Laplace extensions and investigate alternative estimation techniques to enhance predictive accuracy in real-world applications.