You will need to iterate through all of the know theoretical distributions to find the correct distribution to use. In Windows, you may use ExpertFit or EasyFit for Excel.
If you are comfortable with R, you can find the minimum log-likelihood function of each distribution.
http://stackoverflow.com/questions/4290081/fitting-data-to-distributionshttps://stackoverflow.com/questions/4290081/fitting-data-to-distributions
The Kolmogorov-Smirnov, Anderson-Darling, Chi-Squared Goodness-of-Fit Tests should be able to help you.
http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm
Let me know if you need anything else.