The Box-Cox family of power transformations (Box and Cox 1964) is defined by

where λ is a free parameter.
(a) Show that, for each y, g*λ(y) is continuous in A. In particular, show that

(b) Find the function v(θ), the approximate variance of Y, that g*λ(y) stabilizes. (v(θ) will most likely also depend on λ.)
Analysis of transformed data in general and the Box-Cox power transformation in particular has been the topic of some controversy in the statistical literature. See Bickel and Doksum (1981), Box and Cox (1982), and Hinkley and Runger (1984).

if , log y limw"-1)/ = logy.