The New Arctangent-Tangent Distribution: Theory, Simulations, and Practice

This article introduces a novel unit distribution, referred to as the new arctangent-tangent (NAT) distribution. Its fundamental properties are derived, with particular emphasis on the cumulative distribution function, probability density function, and quantile function. Building on this framework, the NAT distribution is further extended to construct a new lifetime distribution, termed the new arctangent-tangent-exponential (NAT-E) distribution. The key properties of this extended distribution are similarly investigated, with a focus on its distributional characteristics and analytical tractability. We introduce five parameter-estimation methods and conduct a Monte Carlo simulation to examine the asymptotic behaviour of the estimators. Finally, the proposed models are applied to real data, where they demonstrate superior performance compared to a certain number of standard models commonly used in the literature.