Modeling of air pollution and Lossalae data by using new classes of skew bivariate family distribution and extreme distributions

Adding two more parameters for shaping provides a flexible way to make any basic bivariate distribution function (df) more adaptable. The extended bivariate dfs can better handle different kinds of bivariate data by including these parameters. They can handle a wide range of skewness and kurtosis indices well. The innovation lies in introducing a novel multiplicative bivariate stable-symmetric normal (MBSSN) distribution with two parameters, extending the conventional bivariate standard normal distribution. We conducted a detailed examination of the statistical properties of the MBSSN family and compared it to other significant competitors, such as generalized families of bivariate dfs, using real-world data like air pollution. The findings underscore the advantages and effectiveness of the MBSSN family in capturing the nuances of diverse datasets. We also applied the same methodology to develop a new two-parameter extension for two variations of bivariate extreme value distributions, which we then useed to analyze Lossalae datasets. This extension showcases the versatility and practicality of the proposed approach across different scenarios and distribution types.