# Modelling the combination of three distributions (not linear combination)

Lets say I want to model a distribution which empirically I can see is a combination of three PDFs in one. For example in the data below you can see a Gamma distribution to the left, a Uniform in the middle, then another (different) gamma to the far right:

Note that this is not simply the addition of three RVs - in some % of the time the RV belongs to Gamma, sometimes Uniform, and sometimes the other Gamma, but not a linear combination of the three. How would be the best way to go about modelling this in pymc3?

I’m not sure if this addresses what I’m trying to do. For example if I had three normal distributions, if I used a mixture the result would be one normal distribution. What I would really want is a distribution with three “peaks” (three superimposed distributions), rather that one distribution which is the result of summing three distributions. Am I misunderstanding the functionality of the link you sent?

Mixture does what you want. It interpolates between the components.

``````import matplotlib.pyplot as plt
import pymc as pm

x = pm.Mixture.dist(
w=[1/3]*3,
comp_dists=[
pm.Normal.dist(-10),
pm.Normal.dist(0),
pm.Normal.dist(10),
],
)
plt.hist(pm.draw(x, 10_000), bins=100)
``````

Edit: I get an error uploading the picture, but you should be able to reproduce on your end