This paper introduces a new one-parameter family (NPFD) derived from the cumulative distribution function (CDF). We study the main properties of the proposed family, with a special emphasis on its moments, reliability parameters, and asymptotic distributions of the extreme order statistics. Then, inferential considerations are explored. We discuss the parameter estimation by the moments, maximum likelihood methods and the Bayesian estimation. Also, likelihood estimation and Bayesian estimation using the Pitman asymptotic criterion are given. Three applications reveal that the new model can fit well practical data sets.