A New Nakagami-Exponential Distribution: Theoretical and Statistical Properties

This article proposes the new Nakagami-generated family of distribution (NNak-G) and the new Nakagami-Exponential (NNak-E) distribution for fitting skewed and heavy-tailed data. By integrating the flexibility of the Nakagami distribution with the useful properties of the exponential distribution, the NNak-E distribution provides enhanced adaptability for fitting with right-skewed data structures. The theoretical properties of the NNak-E distribution are developed, including its distribution function, density function, moments, and hazard function. Parameter estimation is constructed using the Maximum Likelihood Estimation (MLE) method, and a comprehensive simulation study is performed to evaluate the performance of the MLE estimates. Furthermore, the NNak-E distribution is applied to real-world datasets, where it demonstrates superior goodness-of-fit compared to existing distributions. The results confirm that NNak-E is a choice distribution for practitioners and researchers dealing with asymmetric and heavy-tailed data distributions in diverse fields such as engineering, medical research, and risk assessment.