Fitting Beta Distribution Parameters via MLE

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 α_k and β_k.

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