We have a cumulative probability distribution function (cdf), we want to scale it down for using it in anomaly detection. The mapping should look like this.
CDF value: 0.1 ... 0.5 ... 0.9 ... 0.99 ... 0.999 ... 0.9999 ........
Mapped to: 0.001 ... 0.002 ... 0.01 ... 0.2 ... 0.3 ... 0.5 ........
So CDF greater than 0.9 is relevant and then the values should start increasing rapidly. The mapped scale is between 0 to 1, with 0.2 being strong anomaly and 1 being extreme anomaly.
Is there any standard function to scale CDF values, in above described manner?
Also is this a standard Statistics approach, or this approach is used in Anomaly Detection? (Any references will be helpful)