The New Heavy‐Tailed Cosine‐Weibull Distribution: Properties, Simulation, Applications, and Regression Modeling

ABSTRACT The development of flexible probability distributions has become essential for accurately modelling real‐world data. In this study, we introduce a new three‐parameter lifetime model, the New Heavy‐Tailed Cosine‐Weibull (NHTCW) distribution, which extends the Cosine‐Weibull distribution using a heavy‐tailed framework. This extension enhances the model's capacity to capture skewness and tail behavior commonly observed in lifetime and survival data. We derive several statistical properties of the NHTCW distribution, including its ordinary and incomplete moments, quantile and generating functions, and order statistics. Maximum likelihood estimation (MLE) is used to estimate the model parameters, and a simulation study is conducted to evaluate the performance of the estimators in terms of accuracy and consistency. We propose a regression model based on the NHTCW distribution, making its first introduction in this context. The practical usefulness of the proposed distribution is demonstrated through three real‐data applications. Two data sets are related to COVID‐19 mortality rates in Italy and Canada, while the third is related to injury rate data. In all cases, the NHTCW model outperforms several existing distributions in terms of goodness‐of‐fit criteria, underscoring its flexibility and practical relevance.