I have some radiation data with a distribution that looks somewhat bimodal. I am looking for a distribution to fit the data (in a negative log likelihood function which will be minimized using
optim()). I have tried fitting a normal and a beta binomial without much success. I would prefer not to transform my data. Is there a distribution is flexible enough to fit with bimodal data?
I have several climate variables: radiation, temperature and precipitation. I am creating a model for each of them so that I can simulate data from them. I have successfully fit a model to the temperature data using a normal distribution. I have also successfully fit a model to precipitation data using an exponential distribution. The only one I have not been able to fit is radiation.
I am fitting a sine curve to each data set because of the seasonal nature of it, and I am optimizing the curve using the negative log likelihood. The red curve is my rough estimate of where the fitted sine curve should be.
Here is what I am ultimately trying to do: I want to simulate data at the high and low ends of the data cloud (i.e. years with lots of high temperatures and years with lots of low temperatures) to test the sensitivity of a different complex model I am using. I was able to use the normal distribution with temperature data and the exponential with precipitation, but I can't find one to work with radiation data given the slightly bimodal nature of the data.