Exponential Arctan-G Family of Distribution With Properties and Applications

Recent research in univariate probability distributions has primarily focused on the introduction of novel generators, families, and additional parameters to existing distributions. The objective is to identify a flexible, valid, and reliable distribution capable of effectively accommodating data across diverse domains. This article introduces a new family of probability distributions called the exponential arctan (ExAT) family. Within this family, a submodel named ExAT−W is formulated using a one-parameter Weibull distribution as a baseline distribution. The article presents various statistical properties of the proposed distribution, highlighting its unique bimodal hazard rate function. To demonstrate the practical application of the ExAT−W distribution, two examples involving remission times and melanoma data are provided, demonstrating its flexibility, stability, and applicability in real-world scenarios.