Non-Central T Distribution

Probability Density Function (PDF)

Cumulative Distribution Function (CDF) (x ≥ 0)

where

and where Φ is the standard normal CDF, 𝛤 is the gamma function, and 𝛪_z(a, b) is the regularized incomplete beta function.

• Range -∞ < 𝑥 < ∞
• Shape parameter 𝜈 > 0
• Non-centrality parameter 𝜆 > 0