Beta distribution vs beta binomial distribution: alpha and beta

I have been attempting to estimate alpha and beta from a beta binomial distribution given my data. There are R packages like VGAM to do this. I am wondering if there is a difference between estimating these parameters for a beta binomial distribution and if I estimated them for a beta distribution. Is there a way to fit my data to a beta distribution and get the same alpha and beta as when I fit it to a beta binomial distribution?

• The beta-binomial distribution is a distribution over non-negative integers less than the number of trials, while the beta distribution is a distribution on reals in the unit interval. Given data that is either integer- or real-valued, one will be an obviously incorrect substitute for the other. What kind of data do you have? – Sycorax Feb 9 '15 at 17:41

Beta and Beta-binomial are two different distributions. Beta is a continuous distribution (values in the $[0, 1]$ range) while Beta-binomial is discrete (integers from $0$ to $n$). So it is not a good idea to use both distributions to approximate your data since it can be discrete or continuous, but not both.
• You just need estimate $\alpha$ and $\beta$ for the beta-binomial distribution. That gives you the parameters for the underlying beta distribution. – Sycorax Feb 9 '15 at 18:01