Objectives: To investigate the Modified Inverse Weibull Distribution (MIWD) to determine its effectiveness in modelling real customer transaction data, which is often skewed and exhibits heavy-tailed characteristics. Methods: Parameters of the model were estimated using the Maximum Likelihood Estimation (MLE) technique. The model's performance was evaluated using goodness-of-fit measures, such as the log-likelihood (ℓ), Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Kolmogorov–Smirnov (K–S) statistic. The probability density function (PDF), cumulative distribution function (CDF), hazard function, and survival function were derived analytically and visualized with Python to assess model behavior and data alignment. Findings: The MIWD demonstrated a better fit for the customer transaction data than its sub-models and other competing distributions. The estimated probability density function (PDF), cumulative distribution function (CDF), hazard, and survival functions highlighted the model's adaptability in representing both skewness and heavy-tailed characteristics in actual transaction data. Novelty: The main contribution of this study is the empirical validation of the four-parameter MIWD using actual customer transaction data, demonstrating its superiority over established sub-models based on various quantitative criteria. The findings provide compelling evidence that the MIWD is a robust and adaptable alternative for modelling skewed, heavy-tailed transaction and lifetime data, with practical applications in customer behavior analysis, reliability engineering, and risk modelling. Keywords: Modified Inverse Weibull Distribution, Maximum Likelihood Estimation, Customer transaction data, Parameters, Rayleigh distribution
Harif et al. (Thu,) studied this question.