Chen-Burr XII Distribution

Abstract

Survival analysis focuses on modeling the time until an event occurs, where the hazard function determines the flexibility of distributions for modeling lifetime data. The Chen distribution, defined by two positive parameters, can represent monotonically increasing and bathtub-shaped hazard functions. However, it cannot accommodate monotonically decreasing and unimodal (upside-down bathtub) hazard patterns, which are frequently encountered in failure risk and medical survival data. This study aims to construct a more flexible distribution capable of accommodating four hazard shapes: increasing, decreasing, unimodal, and bathtub-shaped using the Transformed-Transformer  method. To address this limitation, the Burr Type XII distribution is used as the transformer distribution due to its ability to capture decreasing and unimodal hazard patterns, while the Chen distribution acts as the transformed distribution. The resulting Chen-Burr XII distribution has four positive parameters . Characteristics discussed in this study are the probability density function, cumulative distribution function, survival function, hazard function, and r-th moment. The maximum likelihood estimation approach is used to estimate parameter values. The Chen-Burr XII distribution is applied to survival data of gastric cancer patients' waiting time to death, exhibiting a unimodal hazard function. Model performance is evaluated using the Kolmogorov-Smirnov test and Akaike’s Information Criterion. The results show that the Chen-Burr XII distribution models data with a lower AIC value compared to the Chen distribution, offering a more flexible alternative for lifetime data with diverse hazard patterns.