The generalized Marshall-Olkin Lomax distribution with applications to AIDS and COVID-19 data

TL;DR

To address flexible lifetime modeling with censoring, the paper introduces the generalized Marshall-Olkin Lomax (GMOL) distribution, defined by the CDF $F(x)=\frac{\lambda G(x) + (1-\lambda) G(x)^2}{\alpha + (1-\alpha) G(x)}$ where $G$ is Lomax. The authors derive a linear representation of the GMOL density in terms of Lomax densities, provide a quantile function, moments, and a generating function, and develop a two-component GMOL regression model for right-censored data estimated by maximum likelihood. Through simulations, the paper confirms estimator consistency and the regression model’s behavior under censoring. In applications to AIDS and COVID-19 survival data, GMOL yields superior fit compared with beta-Lomax, Kumaraswamy-Lomax, Weibull-Lomax, MOL, and Lomax, and the Distrito Federal data demonstrate significant effects of age and obesity on survival.

Abstract

The generalized Marshall-Olkin Lomax distribution is introduced, and its properties are easily obtained from those of the Lomax distribution. A regression model for censored data is proposed. The parameters are estimated through maximum likelihood, and consistency is verified by simulations. Three real datasets are selected to illustrate the superiority of the new models compared to those from two well-known classes.

Figures (6)

• Figure 1: Density and HRF of $X$.
• Figure 2: Skewness and kurtosis of $X$.
• Figure 3: Bonferroni and Lorenz curves of $X$.
• Figure 4: Estimated plots for AIDS data.
• Figure 5: Estimated plots for COVID-19 data (Paraíba).