func:quantile

quantile(percent, method: "linear")

Computes the p*th* quantile of a list of numbers, according to the specified interpolation method. The value p must be a number between 0.0 to 1.0.

• linear (default): Interpolates proportionally between the two closest values
• nearest: Rounds to the nearest data point
• lower: Rounds to the nearest lower data point
• higher: Rounds to the nearest higher data point
• midpoint: Averages two nearest values

Usage:

[1,2,3].fold(quantile(p, method))

Examples:

[10,10,10,25,100].fold(quantile(0.7 )) => 22 //default to linear
[10,10,10,25,100].fold(quantile(0.7, "nearest")) => 25
[10,10,10,25,100].fold(quantile(0.7, "lower")) => 10
[10,10,10,25,100].fold(quantile(0.7, "higher")) => 25
[10,10,10,25,100].fold(quantile(0.7, "linear")) => 22 //same as no arg
[10,10,10,25,100].fold(quantile(0.7, "midpoint")) => 17.5

Detailed Logic:

p: percentile (decimal 0-1)
n: list size
rank: p * (n-1) // this is the index of the percentile in your list
// if rank is an integer, return list[rank]
// if rank is not an integer, interpolate via one of the above methods (illustrated below in examples)

[1,2,3,4,5].percentile(0.5) => 3 // rank=2 is an int so we can index[2] directly

[10,10,10, 25, 100].percentile(0.7, method)
  rank = (0.7 * 4) => 2.8

  //adjust rank based on method
  nearest =  index[3]                // => 25
  lower =    index[2]                // => 10
  higher =   index[3]                // => 25

  //or interpolate for these methods

  //takes the 2 closest indices and calculates midpoint
  midpoint = (25-10)/2 + 10          // => 17.5

  //takes the 2 closest indices and calculates weighted average
  linear =   (0.2 * 10) + (0.8 * 25) // => 22

def	func:quantile
is	func
lib	lib:math
name	quantile

feature	Feature namespace of definitions formatted as feature:name
func	Axon function