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: