How to model distributions which are not normally distributed I would like to model the performance of a rainwater tank, which has a stochastic input (rainfall). The data are the empty volume in the tank at the end of each day. The values are skewed towards the extremes, and I am not sure how to model this or present it statistically. Reviewing various distributions in Wikipedia, I found that it seems like a Beta Distribution - but I am not sure whether it is one. I need to find a statistical method of representing the 'empty volume'.
One friend suggested that I use binomial distribution of getting probability of tank being 25% empty, 50% empty or 75% empty and find confidence intervals associated with those values.
Here is the distribution of my data:

EDIT - 11 July 7:28 GMT (following comments for clarification)
The inflow into the tank occurs randomly due to the rainfall. There is regular abstraction from the tank if there is stored volume. 
I would like to estimate the probability of the empty volume in the tank on any random day in future based on the the historic data, and associated confidence of that probability. 
I would then like to use that 'empty volume' figure to estimate how much of a large storm rainfall it can a large number of such tanks hold back and reduce the flash flooding volumes. Possibly may need to present combined probabilities with the storm probability.
 A: 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.
A: @COOLSerdash's comment is right on target (+1).  It seems unlikely that your data are actually any of the named distributions, such as beta, and the answer by @Glen_b will provide a nice example of how you might go about exploring your dataset.  
The fitdistrplus package in R will provide you with some tools that may be helpful.  For example, if you just want to estimate the parameters of the beta distribution that maximize the likelihood of your data, ?fitdist will help. 
A: "The data are the empty volume in the tank at the end of each day."


*

*The data are time indexed, you have to take this feature into consideration.

*It is likely that the data are dependent. Someone/Something fill up the tank at some time points or when the tank is close to depletion.
I suggest to take a look at Time Series models (e.g. autoregressive models), rather than fitting a distribution to the raw observations, in order to avoid throwing all the features of the data.
The estimation procedures recommended in the other answers do not consider possible dependencies of the data and time indexing.
A: I assume you are trying to find some well known distribution to model your data.  If this is the case, then you could do a goodness of fit test.  This is a well known test and there are several methods.  You will be testing many different distributions to see which one best fits.  Then just pick the one that best works for you.
Not sure what you are doing this for, but you could use an empirical distribution, which is basically just the sample itself.
These methods are easy to look up online.
