A new method for adding parameters to a well-established distribution to obtain more flexible new families of distributions is applied to Lomax distribution (LD). This method is known as the Alpha-Power transformation (APT) and introduced by Mahdavi and Kundu (2015). The reliability and statistical properties of the proposed models are studied. Maximum likelihood method of estimation is utilized to obtain the estimators of the population parameters. The extended model is applied on a real data and the results are given and compared to other models. Also, a bivariate distribution was constructed from the proposed distribution using the Farlie-Gumbel-Morgenstern (FGM) copula. Some characteristics of this distribution and the estimation using the maximum likelihood are shown on a real data.