Processus empiriques des rapports de m-espacements uniformes disjoints (Non-overlapping uniform m-spacings-ratio empirical processes)

الأصل · EN

We consider an empirical process based upon ratio of selected pair of the non-overlapping m-spacings generated by independent samples of arbitrary sizes. As a main result, we show that when both samples are uniformly distributed on intervals of equal lengths, this empirical process converges to a mean-centered Brownian bridge of the form (B∘ Hₘ)C(v)=B(Hₘ(v))-2(2m+1)C(2m-1)!/m((m-1)!)²(v(1-v))ᵐ∫₀¹B(Hₘ(s)) s, for 0≤ v≤ 1, where B(.) denotes a Brownian bridge, Hₘ, the distribution function of the Beta distribution with parameters m and m, and C, a constant.