Nadarajah–Haghighi Lomax Distribution and Its Applications

Abstract

Over the years, several researchers have worked to model phenomena in which the distribution of data presents more or less heavy tails. With this aim, several generalizations or extensions of the Lomax distribution have been proposed. In this paper, an attempt is made to create a hybrid distribution mixing the functionalities of the Nadarajah–Haghighi and Lomax distributions, namely the Nadarajah–Haghighi Lomax (NHLx) distribution. It can also be thought of as an extension of the exponential Lomax distribution. The NHLx distribution has the features of having four parameters, a lower bounded support, and very flexible distributional functions, including a decreasing or unimodal probability density function and an increasing, decreasing, or upside-down bathtub hazard rate function. In addition, it benefits from the treatable statistical properties of moments and quantiles. The statistical applicability of the NHLx model is highlighted, with simulations carried out. Four real data sets are also used to illustrate the practical applications. In particular, results are compared with Lomax-based models of importance, such as the Lomax, Weibull Lomax, and exponential Lomax models, and it is observed that the NHLx model fits better.