Families of parametric functions g(x) for improving data fits of given distribution functions F (x) via distribution functions F (g(x)) are provided. These new distribution functions are called doped distribution functions. They are tailored in function of a given data set by varying g(x). Conditions for guaranteeing that F (g(x)) be a distribution function are discussed. The design F (g(x)) increases nonlinearities in the likelihood function due to the need of supplementary parameters related to g(x). This makes parameter estimation harder and in some cases, with non-unique solutions. This drawback is managed through the use of optimization procedures without calculation of derivatives when parameters are estimated. In spite of this increase in model complexity, examinations on a number of real data sets and known distribution functions put in evidence advantages on the use of these functions g(x), showing in many cases improvements on data fits. Some of these improvements are remarkable .