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)
As for your question about anomaly detection, you can use any threshold on CDF to declare an anomaly, despite what the CDF is, and you can apply any arbitrary non-negative increasing transformation to your CDF. So your proposed framework doesn't really add anything new to the concept of "anomaly detection." You're just changing around some thresholds for detection from one CDF to the next, leaving the set of finally declared "anomalies" intact. And frankly, 0.2 is quite an unusually low threshold to declare an anomaly anyway, at least in practice, so you might want a different pair of transformation/threshold assuming this is something you still want to do and sell to your audience.