The modified odd Burr XII-G family of distributions: Properties and Applications

TL;DR

The paper introduces the MOBXII-G family, a flexible transformation-based extension of baseline distributions via $W[G(x)]=\dfrac{G(x)}{1 - G(x)[1+G(x)]/2}$, enabling bimodal and bathtub hazard shapes. It develops three concrete models—MOBXIIW (Weibull baseline), MOBXIIK (Kumaraswamy baseline), and MOBXIIN (normal baseline)—and derives their CDFs, PDFs, quantile functions, moments, and an exp-G mixture representation to facilitate analysis. A censored regression framework (LMOBXIIW) and maximum likelihood estimation are presented, with simulations confirming estimator consistency. Applications to dengue incidence, length of stay in Japan, and COVID-19 survival data demonstrate superior fit over competing G-family models, highlighting MOBXII-G’s practical value for skewed and multimodal lifetime data and censored analyses.

Abstract

The modified odd Burr XII-G family is developed, capable of incorporating bimodal and bathtub shapes in its baseline distributions, with properties derived from the exponentiated-G class. A regression model is developed within this family. The parameters are estimated by maximum likelihood, and simulations are performed to verify their consistency. The usefulness of the proposals is demonstrated by means of three real data sets.

Figures (9)

• Figure 1: Density and hrf of $\text{MOBXIIW}(\tau,\lambda,\alpha,\beta)$.
• Figure 2: Density and hrf $\text{MOBXIIK}(\tau,\lambda,a,b)$
• Figure 3: Density and hrf of $\text{MOBXIIN}(\tau,\lambda,\mu,\sigma)$.
• Figure 5: Skewness and Kurtosis of $\text{MOBXIIW}(\tau,\lambda,\alpha,\beta)$.
• Figure 6: Boferroni and Lorenz curves of $\text{MOBXIIW}(\tau,\lambda,\alpha,\beta)$.