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Positive random variables X and Y satisfy a scale model with parameters > 0 if P(Y t) = P(X t) for all t > 0, or equivalently, G(t) = F(t/) (a) Show

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)


(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.

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