I am trying to fit a beta distribution to election forecast data. The ultimate purpose is determining with what probability the election will be decided by one vote (more on this here).
My data is as follows:
0.517 0.59 0.55 0.528 0.496 0.51 0.55 0.54 0.57
I use the scipy
scipy.stats.beta.fit() function, as discussed here.
For my data I get:
$\alpha = 0.7469674643946238 $
$\beta = 1.7165349362225657 $
which leads to a sloping distribution with its maximum close to zero.
For most other artificial data I have tried, I get distributions which actually hold water. Obviously, for my case this is wrong (it may not be for others), but I would like to make certain that the minima of the distribution are close to 0 and 1 respectively, and the maximum is approximately in the range of my data points.
I had thought of fitting a normal distribution to my data, and a beta distribution to that - but that would be an approximation of an approximation. I'd rather do it all in one "step".