Beta distribution


Asst Vice President
Hi David
I read that Beta distribution can take any shape. Why so? Why it does not follow normal or lognormal distribution?



David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi Rajiv,

Not quite any shape. De Servigny notes two weakenesses: can't be bi-modal (like a two humped camel) and doesn't handle zero (no recovery) or 1.0 (fully recovery) well. His point is the beta is "flexible" unlike most of the other distributions we look at. Many of the credit portfolio models (e.g., CreditMetrics) use beta distribution owing to its flexibility.

To my knowledge, however, unlike the GEV (mentioned in Wilmott's EVT) which is mathematically derived (it "converges" based on the EVT assumptions), there is nothing "magic" about beta against recoveries. Rather, it is favored for two reasons:

1. flexible (i.e., to fit various scenarios)
2. compact; only need bounds and two params

I am frankly not expert on beta distribution - it is related to binomial/gamma, and I *think* with certain params it may converge it to the others but i cannot recall exactly...