Asymmetric generalized error distribution with its properties and applications

Abstract

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 this distribution the asymmetric generalized error distribution (AGED). AGED is a new contribution to the field of statistical theory, offering more flexible probability density functions, cumulative distribution functions, and hazard functions 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 the parameters of the distribution are obtained using the maximum likelihood approach. In a 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 cybersecurity domains, the performance of the new distribution is compared to that of other distributions. The new distribution is found to be a better fit for the data, showing great adaptability in the context of real data analysis. We expect the distribution to 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.