Generalized Error Distribution

Generalized Error Distribution

Probability Density Function (PDF)

Cumulative Distribution Function (CDF)

where 𝛤(𝛽) is the Gamma function and 𝛾(𝑘, 𝑧) is the lower incomplete Gamma function.

Range -∞ < 𝑥 < ∞

Location parameter 𝜇

Scale Parameter 𝛼 > 0

Shape parameter 𝛽 > 0

Notes: This is also known as the Exponential Power distribution or the Generalized Normal distribution.