It is widely used to model the polydispersity of polymers.

In this context it has been introduced in 1939 by Günter Victor Schulz[1] and in 1948 by Bruno H.

[2] This distribution has only a shape parameter k, the scale being fixed at θ=1/k.

Accordingly, the probability density function is

When applied to polymers, the variable x is the relative mass or chain length

is just a gamma distribution with scale parameter

This explains why the Schulz–Zimm distribution is unheard of outside its conventional application domain.

For large k the Schulz–Zimm distribution approaches a Gaussian distribution.

In algorithms where one needs to draw samples

, the Schulz–Zimm distribution is to be preferred over a Gaussian because the latter requires an arbitrary cut-off to prevent negative x.