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Abstract Let {Xni,1≤i≤mn,n≥1} $\{X_{ni}, 1 \leq i \leq m_{n}, n\geq 1\}$ be an array of independent random variables with uniform distribution on [0,θn] $[0, \theta _{n}]$, and {Xn(k),k=1,2,…,mn} $\{X_{n(k)}, k=1, 2, \ldots , m_{n}\}$ be the kth order statistics of the random variables {Xni,1≤i≤mn} $\{X_{ni}, 1 \leq i \leq m_{n}\}$. We study the limit properties of ratios {Rnij=Xn(j)/Xn(i),1≤i<j≤mn} $\{R_{nij}=X_{n(j)}/X_{n(i)}, 1\leq i < j \leq m_{n}\}$ for fixed sample size mn=m $m_{n}=m$ based on their moment conditions. For 1=i<j≤m $1=i < j \leq m$, we establish the weighted law of large numbers, the complete convergence, and the large deviation principle, and for 2=i<j≤m $2=i < j \leq m$, we obtain some classical limit theorems and self-normalized limit theorems.