I have some solar power plants data where the response I am trying to predict is its performance (usually a percentage from 0 to 100%), specifically the probability of it performing at under a particular (e.g. 98%, 95%) performance. For every plant site, I have about 24 data points of historical performance (monthly, weather-adjusted for the past 2 years). My current approach is fitting a normal distribution, but 1) data is very skewed as most performance is between 90 to 100% and 2) I am not sure if my approach is statistically sound, as a plant may have straight 100% performance for 20 out of the 24 months I have data for-then I can't really imagine fitting a normal curve. Would like to achieve this using R. Any help appreciated. Thank you!
There is a large number of possible distributions to fit. Beta-distribution might suit your needs, as it is constrained to values between 0 and 1 (so 0 % and 100 %) including both borders.
curve(dbeta(x, 50, 1))
to see if that is in the right ballpark for your data.
A different approach might be bootstrapping. You cannot bootstrap additional observations but you could bootstrap means of a number of possible observations, if that is of any help for your problem.
24 observations contain only so much information and you are obviously right, that there will be a lot of uncetrainty about your result. You will have to decide on the real world problem whether there is a chance of sampling more data and if not, whether it is a good or a bad thing to compute such an uncertain prediction.
In Bayesian statistics people value the knowledge they have before sampling the data and they formalize it as the "prior". Without getting to deep into Bayesian data analytics: You have prior knowledge about the functioning of a solar power plant. You know that it will not function at an always 100% rate and you know, that it is very unlikely to work below 90% in the median and you suppose its risk of running at 0% is less then 5%. So if there really is 24 observations at 100% don't predict 100% for all future. You should decide and write down how to go on with your data before you start sampling. One way might be to add one 0% value and one 100% value to your observations just because you knew before, that 0% and 100% values have been observed in the past.