Four-parameter Beta distribution/PERT distribution

[barabadzhi]

Background

What is your motivation?

Statistical computing.

What type of application is this? (E.g. cryptography, game, numerical simulation)

Simulation.

Feature request

Will be really nice to have four-parameter Beta distribution/PERT distribution in place. It offers an alternative to using the triangular distribution which takes the same parameters. The PERT distribution has a smoother shape than the Triangular distribution yielding extremes less frequently.

[dhardy]

Thanks for the suggestion. Can you point us to any sampling algorithms for the distribution?

[barabadzhi]

@dhardy

Here are some references:
R
Python
C

Hope, they can be helpful 🙂

[dhardy]

Thanks! Question: why is this typically parameterised by (min, max, mode, mode_weight) and not by (min, max, mean)? It looks like it would be easy to add constructors for each if desired.

I guess also it's common to use (min, max) = (0, 1)?

[barabadzhi]

Mean is the average of all observations.
Typically we use PERT distribution when there are a few observations (thus mean is impractical), but we have min, max and "the most likely value" (mode) instead. We also use mode weight to affect the shape of the curve.

Min/max values can be whatever. I'm generating customer demand data in XXX tons for example. And this can be from 0.1 ton to 10K ton. But (0,1) as default values are fine to me 🙂

[dhardy]

Okay, I'll start on this soon, but it's currently blocked by #770.