### 8.2.5 Specific Rank Tests Using Approximate Scores

First, note that the scores ${a}_{N}\left(i,f\right),{a}_{1N}\left(i,f\right),\dots$ can only be obtained from tables (if available) due to their complicated expressions. For example, there are tables for $\text{E}\left[{\Phi }^{-1}\left({U}_{N:i}\right)\right]$. However, since $\text{E}\left[{U}_{N:i}\right]=i/\left(N+1\right)$ and $\text{Var}\left[{U}_{N:i}\right]=i\left(N-i+1\right)/\left\{{\left(N+1\right)}^{2}\left(N+2\right)\right\}\to 0$ as $N\to \infty$, the distribution of UN:i is concentrated near i

Get Theory and Methods of Statistics now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.