Student's T Distribution with Location

Student's T Distribution with Location and Scale

Probability Density Function (PDF)

Cumulative Distribution Function (CDF)

where

and where 𝛤 is the gamma function, and 𝛪z(𝑎, 𝑏) is the regularized incomplete beta function

Range -∞ < 𝑥 < ∞

Location parameter 𝜇

Scale parameter 𝛼 > 0

Shape parameter 𝜈 > 0