Metalog Distributions


I am looking to use Metalog Distributions (1 1 The Three Types of Probability Distributions - YouTube) in a project I’m working on.

Are there any packages that have implemented them (including fitting to data, and adding/multiplying random variables that are metalog distributed )? If not and I wanted to port the equations to julia, how would I do it (in a way that works well with julia’s other statistics libraries)?

Something like:

d = SPTMetalog(low=0, mid =15, high=20)
d2 = SPTMetalog(low=2, mid=13, high=35)


d3 = d + d2
> Metalog(.... [a function generated from mean/skewness/kurtosis per the formula on the website])
sample(d3, 100) # uses quantile function form to generate simulation
> Vector{Real} [ 24, 2, 23, 34, 1, 2, 20, 14, 5, 15, .....]