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

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).]