In this work we introduce a wide family of continuous univariate distributions with support \((0,\infty )\) that includes as special cases the majority of classical continuous distributions. The new family contains distributions with cumulative distribution function of the form \(F(x;\varvec{\theta })=g^{-1}(h(x;\varvec{\theta }))\) , where g and h satisfy specific conditions. We study its properties, including aging, tail properties and unimodality, and apply our general results to families of classical distributions, thereof obtaining alternative proofs of well known results. We also discuss how the new framework can be exploited for the generation of new distributions that possess specific desirable properties (e.g. they have heavy tails, monotone failure rates etc).
