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## Sunday, October 19, 2014

### prob integral transform (percentile), intuitively

I find the PIT concept unintuitive ...Here's some learning notes Based on http://www.quora.com/What-is-an-intuitive-explanation-of-the-Probability-Integral-Transform-aka-Universality-of-the-Uniform answer by William Chen.

Let's say that we just took a midterm (or brainbench or IKM) and the test scores are distributed according to some weird distribution. Collect all the percentile numbers (each between 1 and 100). Based on PIT, these numbers are invariably uniformly distributed. In other words, the 100 "bins" would each have exactly the same count! The 83rd percentile students would tell you

"82% of the students scored below us, and 17% of the students scored above us, and we are exactly 1% of the batch"

Treat the bins as histogram bars... equal bars ... uniform pdf.

The CDF is like the percentile function, which accepts a score and returns the percentile, an integer between 1 and 100.