Home / Questions / Positive random variables X and Y satisfy a scale model with parameters δ 0 if PY t PδX...
Positive random variables X and Y satisfy a scale model with parameters δ > 0 if P(Y ≤
t) = P(δX ≤ t) for all t > 0, or equivalently, G(t) = F(t=δ), δ > 0, t > 0.
(a) Show that in this case, log X and log Y satisfy a shift model with parameter log δ.
(b) Show that if X and Y satisfy a shift model with parameter ∆, then eX and eY satisfy a
scale model with parameter e∆.
(c) Suppose a scale model holds for X, Y . Let c > 0 be a constant. Does X' = Xc, Y' = Yc
satisfy a scale model? Does log X', log Y' satisfy a shift model?
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