I have a set of observations of credit loss data, where the mean is 37% and variance 25%. Now, I have to find the distribution and the base assumption is it will follow a beta distribution. the issue is that my alpha and beta derived from mean and variance is being estimated at -0.025012 and -0.042588. I dont understand what to do with the negative values of alpha and beta. The formula which I am using to calculate alpha is mean*(((mean*(1-var))/var)-1) and beta is calculated by (1-mean)(((mean*(1-mean))/var)-1). Please do let me know how can I solve the problem.
Partially answered in comments:
Your results are correct. The interpretation is that there is no Beta distribution with this mean and variance. BTW, variance cannot be "25%"; its units need to be squared percent. If the value of 0.25 is really the standard deviation, then the matching parameters are $(a,b) = (1.01,1.72)$. If indeed the values you give are the mean and variance, though, then you ought to change your question to "how can I best estimate parameters of a Beta distribution from data and check the resulting goodness of fit." – whuber
( @whuber - the variance is indeed 0.25. Thanks for the help. The answer looks simple, but I could not find it online. Can you please tell me where I may get hold of the argument as i plan to refer to it in the model document. – Bik )