Basic Concepts
We show how to estimate the parameters of the beta distribution using the maximum likelihood approach. From the pdf of the beta distribution (see Beta Distribution), it is easy to see that the log-likelihood function is
We now define the following:
where ψ and ψ1 are the digamma and trigamma functions, as defined in Fitting Gamma Distribution using MLE.
Newton’s Method
We can now use Newton’s Method to estimate the beta distribution parameters using the following iteration:
where all these terms are evaluated at αk and βk.
Examples Workbook
Click here to download the Excel workbook with the examples described on this webpage.
Reference
Wikipedia (2017) Beta distribution
https://en.wikipedia.org/wiki/Beta_distribution
Thanks a lot for the explanation and the spreadsheet. I created a copy in Numbers on the Mac.
Could you post a screenshot of the Excel sheet. That would allow me to check whether my implementation gives the correct results,
tnx,
Arnaud
Hello Arnaud,
If you click on the Download button towards the bottom of the webpage, you can download the spreadsheet with the example. You can then take a screenshot of the example if you like.
Charles