To generate a functional form totally independently from only a dataset is pretty much not feasible.
There are a number of general distribution families; the Johnson and Pearson are two of the more commonly used.
Selection of one of the candidate families begins by computing (commonly "beta1" and "beta2") measures of skewness and kurtosis and seeing where on a generalized chart of b1,b2 the particular data sample lies and using that to select a potential candidate distribution family.
It must be noted, however, this is no magic panacea that can be applied blindfolded...
Hahn & Shapiro, Statstical Models in Engineering, Wiley, Chapters 6,7 is a good introductory text.
