A new probabilistic method for the generation of asymmetrical distributions: Empirical analyses using asymmetrical data

Considering the significance of asymmetric statistical distributions in applied fields, this paper proposes a new statistical technique to enhance the distributional adaptability of conventional models. The proposed methodology can be referred to as the new amended sine-G (NAS-G) method. The NAS-G method is capable of producing asymmetrical probability distributions. Using the NAS-G framework, an enhanced version of the Weibull model, namely, a new amended sine Weibull (NAS-Weibull) distribution, is examined. The NAS-Weibull distribution can effectively represent asymmetric shapes in its density function and support various settings in its hazard function. The maximum likelihood estimators of the NAS-Weibull distribution are obtained. Furthermore, a simulation analysis is conducted to investigate the behavior of these estimators. Moreover, properties based on quartiles of the NAS-Weibull distribution are also obtained. Finally, two asymmetric data sets obtained from the fields of finance and engineering are analyzed with the aim of illustrating the NAS-Weibull distribution in practical contexts. Utilizing four information criteria and a recognized goodness-of-fit test in addition to the p-value, we find that the NAS-Weibull distribution outperforms some adversarial distributions. Our results indicate that the NAS-Weibull distribution could serve as an effective candidate distribution for examining real-world data in finance, engineering, biomedical areas, environmental sciences, hydrology, and management sciences, among others.