Novel DUS Topp-Leone Burr-Hatke exponential model with properties and application to COVID-19 datasets

Abstract

This study presents the DUSTopp-Leone Burr-Hatke-Exponential (DUSTL_BHE) model, a new and more flexible extension of the BHE model.  The DUSTL_BHE model accommodates diverse density shapes such as right-skewed, heavy-tailed, unimodal, or decreasing, and failure rate patterns such as increasing, decreasing, inverted-bathtub, and reversed-J. Several statistical properties, including raw and incomplete moments, quantile and moment-generating functions, entropies, and order statistics, are derived and illustrated. The DUSTL_BHE model parameters are estimated using the maximum likelihood estimation (MLE) method. Simulation studies were utilized to assess the accuracy and efficiency of the MLE, while three real datasets from medical and engineering applications demonstrate the model’s flexibility.  The DUSTL_BHE model is compared with several competing distributions using standard goodness-of-fit criteria such as the log-likelihood, Akaike information criterion (AIC), Bayesian information criterion (BIC), corrected AIC (AICc), Hannan Quinn IC (HQIC), and Kolmogorov–Smirnov (KVS) statistics. The results show that the DUSTL_BHE distribution provides smaller AIC, BIC, AICc, HQIC, and KVS values and higher log-likelihood values than the competing models, indicating a superior fit to the datasets. These findings demonstrate that the DUSTL_BHE model is a flexible and useful alternative for modelling skewed and heavy-tailed real-world data, particularly in epidemiological and reliability studies.