Let G(x) = G0 ³ x−θ δ ´ , θ ∈ R1, δ ∈ R + 1 and G0 does not depend on (θ,δ). Then show that                         G −1 (3/4) − G −1 (1/4) = δ{G −1 0 (3/4) − G −1 0 (1/4)} = δT(G0), where the...

Let G(x) = G0 ³ x−θ δ ´ , θ ∈ R1, δ ∈ R + 1 and G0 does not depend on (θ,δ). Then show that

                        G −1 (3/4) − G −1 (1/4) = δ{G −1 0 (3/4) − G −1 0 (1/4)} = δT(G0),

where the functional T(G0) does not depend on (θ,δ). Study the nature of T(G0) for G0 normal, Laplace, and Cauchy, and comment on the errors in the definition of the interquartile range if the true F0 and assumed G0 are not the same.