The Flexible Nadarajah–Haghighi Distribution: Properties, Inference, and Applications

Abstract

This article explores a flexible extension of the Nadarajah–Haghighi (NH) model, referred to as the odd inverse Pareto Nadarajah–Haghighi (OIPNH) distribution. We derive the mathematical properties of the probability density function of the OIPNH distribution, which exhibits a variety of behavior shapes, including decreasing, increasing, J-shaped, reversed J-shaped, bathtub, upside-down bathtub, and decreasing-increasing-decreasing hazard rates. Additionally, the distribution can display right-skewed, symmetrical, and concave-down densities. The parameters of the OIPNH distribution are examined using eight classical estimation approaches. We present extensive simulation results to evaluate the performance of these methods for both small and large sample sizes. Furthermore, we analyze three real-life datasets from engineering, medicine and agricultural sciences, demonstrating the flexibility of the OIPNH distribution compared to existing NH distributions.