Arctan inverted exponentiated Weibull model with actuarial measures and applications to insurance and inflation data

Trigonometric-based statistical models have gained attention in recent years because of their ability to capture complex data patterns. In this article, we propose a new extension of the inverted exponentiated Weibull (IEW) distribution by embedding it within the arctan-X generalized family. The new model, called the Arctan Inverted Exponentiated Weibull (ATIEW) distribution, has flexible density and hazard function, making it suitable for different types of data. Several statistical properties are derived, including quantiles, moments, generating functions, incomplete and conditional moments, as well as actuarial risk measures. Parameter estimation is carried out using seven classical methods, and the performance of the estimators is examined through simulation. The model is also applied to empirical datasets to illustrate its practical use.