The Gudermannian Generated Family of Distributions with Characterizations, Regression Models and Applications

This study proposes a new family of continuous distributions, called the Gudermannian generated family of distributions, based on the Gudermannian function. The statistical properties, including moments, incomplete moments and generating functions, are studied in detail. Simulation studies are performed to discuss and evaluate the maximum likelihood estimations of the model parameters. The regression model of the proposed family considering the heteroscedastic structure of the scale parameter is defined. Three applications on real data sets are implemented to convince the readers in favour of the proposed models.