Using Beta Distribution for Estimating Recovery Rates

Most of the people use the beta distribution to model recovery rates.

In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval (0, 1) parameterized by two positive shape parameters, typically denoted by α and β.

The function for the beta distribution is as follows:

$f(x)=c.x^{a}(1-x)^{b}$

c is the normalization constant.

We can input different values of α and β to obtain different shapes of recovery rates.

The mean and standard deviation of the dataset can be used as the two parameters α and β of the beta distribution using the BETADIST() function in excel. The following graph shows four shapes of the curves based on the different values of mean and standard deviation.