Pearson Law 

The Pearson law is parameterized by (no unit). Another name for the Pearson law is Chi-squared law.
If random variables follows the Normal law with mean 0 and variance 1, then:
 
 
  Let's take a random variable following the Pearson law, then:

is distributed according to the following density of probability, where:

 

And where is a Gamma function.

With mean:

 

With variance:

 

With standard deviation: