BoxCox Distribution Threshold

Probability Density Function (PDF)

Cumulative Distribution Function (CDF)

Range 0 < 𝑥 - 𝜃 < ∞

Location parameter, 𝜇, the mean

Scale parameter, 𝜎 > 0, the standard deviation

Shape parameter 𝜆

Threshold parameter 𝜃 < 𝑚𝑖𝑛(𝑥)

Notes: The concentrated likelihood is used in the ML estimation. This implies that the location and scale parameters are not estimated freely, but are derived as the mean and standard deviation of the BoxCox transformed variate.