초록
In this paper, we establish some characterizations which is satisfied by the independence of the upper record values from the Pareto distribution. We prove that $X\;{\in}\;PAR(1,\;{\beta})$, $\beta$ > 0, if and only if $\frac{X_{U(n)}}{X_{U(m)}}$ and $X_{U(m)}$, $1\;{\le}\;m\;<\;n$ are independent. We show that $X\;{\in}\;PAR(1,\;{\beta})$, $\beta$ > 0 if and only if $\frac{X_{U(n)}+X_{U{(n+1)}}}{X_{U(n)}}$ and $X_{U(n)}$, $n\;{\ge}\;1$ are independent. And we characterize that $X\;{\in}\;PAR(1,\;{\beta})$, $\beta$ > 0, if and only if $\frac{X_{U(n)}}{X_{U(n)}+X_{U{(n+1)}}}$ and $X_{U(n)}$, $n\;{\ge}\;1$ are independent.