quantile

quantile, function

def pure quantile(d: ranvar, p: number): number

Returns the pth quantile of the ranvar d; the smallest integer $k$ such that $\mathbf{P}[d \leq k] \geq p$.

• d: the ranvar representing the probability distribution from which to compute the quantile.
• p: the quantile to be computed, as a number between 0 and 1.

Example

table T = with
  [| as P |]
  [| 0.1  |]
  [| 0.5  |]
  [| 0.75 |]
  [| 0.99 |]
  [| 1    |]

show table "" a1b4 with
  T.P as "P"
  quantile(poisson(3), T.P) as "Quantile"

This outputs the following quantile table:

Remarks

Calling quantile with p=0 and p=1 will return the minimum and maximum of the distribution, respectively.

An example of a use case for quantile(d, 1) is to build safeguards on the output d of a probabilistic demand forecast, by comparing quantile(d, 1) with the maximum consumption ever seen on a time window equal to the forecasting horizon, to check whether there is a risk of overforecast.

Errors

Calling quantile with a parameter p outside of $[0, 1]$ is not supported and results in an error message :

‘quantile(d,p)’ : invalid value 2 for p, should be in [0, 1].