The image below shows the cumulative distribution of a normal distribution with mean = 4 and standard deviation = 1. Notice that if you have a value with a rank of 0.8 (meaning it would be 80th item from the bottom in a sorted list of 100 items) you could get the corresponding value from the CDF of a normal distribution of any mean/sd (if you knew how to do it). I'll bet there is a nice way to do this. I can only think of overly complicated, never do it what way! ways.
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Either InverseCDF
or Quantile
may be used to find the population/data cutoffs (or quantiles) corresponding to given cdf level. The functions are Listable
, too.
Both
InverseCDF[NormalDistribution[4, 1], Range[0.1, 0.9, 0.1]]
and
Quantile[NormalDistribution[4, 1], Range[0.1, 0.9, 0.1]]
yield the deciles for the example normal distribution.
(* {2.71845, 3.15838, 3.4756, 3.74665, 4., 4.25335, 4.5244, 4.84162, 5.28155} *)
InverseCDF
? $\endgroup$ – Michael E2 Nov 2 '13 at 15:01