Finding parameters of a Generalized Beta distribution of the second kind

[Jacques]

Hi,

I have historical data for a ratio, and I need to find the corresponding GB2 parameters, a, b, p and q (respectively location, scale, skewness and kurtosis).

I tried to do it in Excel, after creating my histogram, I see clearly that the distribution has the shape of the generalized beta distribution of second kind (GB2).
Tried to use excel function (mean, std, kurt and skew, with transforming mean and std to 'a' and 'b' - method of moments) but when I plug all my parameters and graph the function, it is absolutely not looking like my histogram. I must be doing something incorrectly

Could anyone help me with this, I will much apppreciate it. (tools availables:excel, SAS, Mathematica, S-Plus)

Thanks !

 

[doug reich]

Can you post the sheet here?

 

[Jacques]

Hi,

yes here it is,

 

[doug reich]

I don't know anything about these functions... but looking at wikipedia, you seem to have misapplied the formulas for alpha and beta: Beta distribution - Wikipedia, the free encyclopedia

I'll play with it a little and if I find the problem I'll post back here.

EDIT: Again, not knowing anything about these distributions, see attached.

 

[Jacques]

Thanks Doug !,

I will drill down further to see how you approached this, the shape looks good though.

Thank you for your help and time,

Jacques

 

[doug reich]

Just a quick note: the changes I made were to adjust the formulas for alpha and beta closer to wikipedia's. Then I tried to create the PDF using the excel functions (if you have a more accurate way of getting the PDF from the CDF values than just taking finite differences, let me know!)