Asymmetric generalized error distribution with its properties and applications - Abebe, Tayu Nigusie; Goshu, Ayele Taye (Frontiers in Applied Mathematics and Statistics, 2024)
The main finding of this study is the derivation of a new probability distribution that reveals interesting properties, especially with various asymmetry and kurtosis behavior; we call it the asymmetric generalized error distribution (AGED). AGED is a new contribution to the field of statistical theory and provides a more flexible pdf, cdf and hazard function than the base distribution. The AGED also includes normal, uniform, Laplace, asymmetric Laplace, and generalized error distribution (GED) as special cases. The mathematical and statistical features of the distribution are derived and discussed. Estimators of parameters of the distribution are obtained using the maximum likelihood approach. With simulation study, random samples are generated from the new probability distribution to illustrate what ideal data looks like. Using real data from diverse applications such as health, industry, and cyber security domain, the performance of the new distribution is compared to other distributions. The new distribution is found to be a better fit for data, and showing a great adaptability in the context of real data analysis. We expect the distribution can be applied to many more real data and the findings of the study can be used as a basis for future research in the field.