On the Completeness of Order Statistics
On the Completeness of Order Statistics
Let $X_1, X_2, \cdots, X_n$ be a sample of a one-dimensional random variable $X$; let the order statistic $T(X_1, X_2, \cdots, X_n)$ be defined in such a manner that $T(x_1, x_2, \cdots, x_n) = (x^{(1)}, x^{(2)}, \cdots, x^{(n)})$ where $x^{(1)} \leqq x^{(2)} \leqq \cdots \leqq x^{(n)}$ denote the ordered $x's$; …