Let X1,...,Xm and Y1,...,Yn be independent samples from I(, ) and I(, ) respectively. (i) There

Let X1,...,Xm and Y1,...,Yn be independent samples from I(µ, σ) and I(ν, τ ) respectively.

(i) There exist UMP unbiased tests of τ2/τ1 against one- and two-sided alternatives.

(ii) If τ = σ, there exist UMP unbiased tests of ν/µ against one- and two-sided alternatives.

[Chhikara (1975).]