Integral, Measure and Martingale: ranking and empirical distributions

2017年8月6日星期日

ranking and empirical distributions

In the absence of repeated values (ties), the cdf can be obtained computationally by sorting the observed data in ascending order, i.e., $X_{s} = \{x_{(1)}, x_{(2)}, \ldots , x_{(N)}\}$ . Then $F(x)=(n_x)/N$ , where $(n_x)$ represents the ascending rank of $x$ . Likewise, the p-value can be obtaining by sorting the data in descending order, and using a similar formula, $P(X \geqslant x) = (\tilde{n}_x)/N$ , where $(\tilde{n}_x)$ represents the descending rank of $x$ .

https://brainder.org/2012/11/28/competition-ranking-and-empirical-distributions/