The Modified Weibull–Fréchet Mixture distribution for enhanced econometric data modelling

This study proposed the Modified Weibull–Fréchet Mixture (MWFM) distribution, which has the ability to model diverse datasets and its applicability in various fields, particularly for modelling econometric datasets. The interpretability of the MWFM distribution is enhanced by its parameters, α and β, where α determines the shape of the distribution and β controls the scale parameter, facilitating meaningful inference and parameter estimation in statistical analysis. The objectives of the study include to: derive the probability density function (PDF) and cumulative density function (CDF) of the MWFM distribution to establish its mathematical foundation; determine the statistical properties of the MWFM distribution, including moments, skewness, and kurtosis; ascertain the reliability characteristics of the MWFM distribution, providing insights into its performance in modelling reliability and survival data; and compare, on a theoretical basis, the statistical properties of the MWFM distribution with existing distributions to highlight its unique features. The study used secondary data to evaluate the performance of the distribution. Model fit was evaluated by comparing the MWFM distribution with existing distributions using metrics such as the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The Modified Weibull–Fréchet Mixture (MWFM) distribution emerges as a formidable contender across various datasets, particularly excelling in modelling tax revenue data. While it ranked lower in certain cases, such as employment in iron sheet jobs and repairs of airborne communication transceivers, the MWFM distribution consistently demonstrated robust performance. The analysis showed that the Fréchet (F) distribution provided the best fit for the data on jobs involving iron sheet production and the active repairs of airborne communication transceivers, achieving the lowest AIC values of 0.3346 and 8.6940, respectively. In these contexts, the Modified Weibull–Fréchet Mixture (MWFM) model ranked fourth and second. However, the MWFM model excelled in modelling tax revenue data, recording the lowest AIC of 63.17527, surpassing the Fréchet distribution. This demonstrates the MWFM distribution’s strong capability to capture complex data patterns, particularly in tax revenue scenarios. The findings suggest that the MWFM model is a viable and effective tool for decision-making processes across various industries, with the potential for further research to enhance its applicability to more diverse datasets