I hope that this question has not already been asked.
I am analyzing data in R (and am a novice).
I have a highly skewed data vector in a dataframe with missing values that I hope to set as the dependent variable in a regression. The values in this vector are skewed because it has a polarizing response tendency (its range is from 1 to 7, but mostly receives very low response values). To proceed, I intend to fit an appropriate distribution to this data and then account for missing data (perhaps via MI or FIML).
Here is the data:
And here is what a Cullen and Frey graph suggests (via the descdist function):
For this data, the Tukey Ladder of Powers does not produce a normal distribution. I was considering fitting a negative binomial or Poisson distribution to the data (which barely gives normally-distributed data), but I think this violates the assumptions of these distributions because my data is not count data. Although a beta distribution is suggested by the graph, I think that my data does not fit the assumptions of this distribution either (its range extends beyond 0 and 1). I was considering that a correctly attuned (correctly-set α and β values) inverse gamma distribution might be the way to go (as can be observed in this website: https://distribution-explorer.github.io/continuous/inverse_gamma.html).
Of course, these considerations are speculative—I don't know how to correctly proceed. Any suggestions would be greatly appreciated.