I would recommend a semiparametric model such as the proportional odds model. This nicely handles data clumping. The model will have one intercept per unique $Y$ value, less one. In two days there will be a major update to the R rms package containing a new ordinal regression modeling function orm that uses sparse matrix algebra to efficiently handle continuous $Y$ (thousands of intercepts). Chapter 15 of my latest course notes contains a case study - see http://biostat.mc.vanderbilt.edu/CourseBios330 and click on Handouts. orm handles 4 other distribution families besides the logistic.

I would recommend a semiparametric model such as the proportional odds model. This nicely handles data clumping. The model will have one intercept per unique $Y$ value, less one. In two days there will be a major update to the R rms package containing a new ordinal regression modeling function orm that uses sparse matrix algebra to efficiently handle continuous $Y$ (thousands of intercepts). Chapter 15 of my latest course notes contains a case study - see http://biostat.mc.vanderbilt.ede/rms and click on Course Notes. orm handles 4 other distribution families besides the logistic.