The Modified-Lomax Distribution: Properties, Estimation Methods, and Application

This paper introduces a flexible three-parameter extension of the Lomax model called the odd Lomax-Lomax (OLxLx) distribution. The OLxLx distribution can provide left-skewed, symmetrical, right-skewed, and reversed-J shaped densities and increasing, constant, unimodal, and decreasing hazard rate shapes. Some mathematical properties of the introduced model are derived. The OLxLx density can be expressed as mixture of Lomax densities. The OLxLx parameters are estimated by using eight estimation methods and their performance is explored by using detailed simulation studies. The partial and overall ranks of the mean relative errors, absolute biases, and mean square errors of different estimators are presented to choose the best estimation method. The flexibility and applicability of the OLxLx distribution is shown using real-life medicine data, illustrating the superior fit of the OLxLx distribution over other competing Lomax distributions. The OLxLX distribution outperforms some rival Lomax distributions including the Kumaraswamy-Lomax, McDonald-Lomax, Weibull-Lomax, transmuted Weibull-Lomax, exponentiated-Lomax, Lomax-Weibull, modified Kies-Lomax, Burr X Lomax, beta exponentiated-Lomax, odd exponentiated half-logistic Lomax, and transmuted-Lomax distributions, among others.

Automated summary

This paper introduces a flexible three-parameter extension of the Lomax model called the odd Lomax-Lomax (OLxLx) distribution, which can provide various shapes of densities and hazard rate shapes. The mathematical properties of the introduced model are derived and the OLxLx parameters are estimated using eight estimation methods. The performance of these estimation methods is explored through simulation studies and the superiority of the OLxLx distribution over other Lomax distributions is demonstrated using real-life medicine data.