A tangent DUS family of distributions with applications to the Weibull model

This study introduces a new trigonometric-based family of distribution by superimposing the Dinesh–Umesh–Sanjay (DUS) transformer in the tangent family of distributions. The resulting family is named Tangent DUS and this new family was utilized to provide a more flexible Weibull (TDUSW) distribution having the same two parameters (parsimony) as the classical Weibull distribution. The parameters were estimated using both non-Bayesian and Bayesian procedures. Furthermore, Monte Carlo simulation study was implemented to determine the behavior of the estimators in the presence of small and large sample sizes. To demonstrate the usability of the model, four datasets namely; the tensile strength of carbon fibers, total factor productivity (TFP) which represent agricultural production growth for thirty-seven African countries from 2001–2010, BTC-USD total weekly amount traded (volume) from June 11, 2021 to June 11, 2024, and HIV/AIDS mortality rate in Germany from year 2000 to 2020 were utilized with the proposed TDUSW distribution having largest p-values as 0.9007, 0.9856, 0.7264 and 0.9832 respectively. In the first two datasets, the TDUSW also has the least values of the metrics of model performance namely AIC, CAIC, BIC and HQIC and also competes favorably in the remaining two datasets. These results show that the proposed TDUSW distribution is superior and possesses some competitive advantage over other existing trigonometric-based models.