A method for generating distributions with an application to Cauchy distribution

There are numerous transformation methods which are in use right now. In this article, the newly proposed model is achieved by using the transformation method known as beta transformation where it does not require more than one additional parameters to the baseline distribution which absolutely is an advantage. The model considered in this article as baseline model is Cauchy distribution with two parameters referred as beta transformed Cauchy distribution (BTC). A comprehensive mathematical treatment of the new proposal is provided. Parameters of BTC distribution are estimated by the method of Cramer-von-Mises, method of maximum likelihood, Anderson Darling, and least square estimation. Simulation study has been carried out to assess the behavior of these estimates. Finally, we considered a real-life data set to illustrate the importance of the proposed distribution and compare with different transformation of distribution where Cauchy distribution as the baseline distribution. This application of a real-data sets shows the performance of the new model over other generalizations of Cauchy distribution.