Contributions to the Theory of Rank Order Statistics--The One-Sample Case
Contributions to the Theory of Rank Order Statistics--The One-Sample Case
The one-sample problem is considered using techniques developed earlier [2], [3]. Let $Z = (Z_1, \cdots, Z_N)$ be a random vector with $Z_i = 1(0)$ if the $i$th smallest in absolute value in a sample of $N$ from the density $f(x)$ is positive (negative). Then $$P(Z = z) = N! …