Calculate Percentile(s) in Bash

Question

I am trying to calculate a range of percentiles (5th-99th) in Bash for a text file that contains 5 values, one per line.

Input

34.5
32.2
33.7
30.4
31.8

Attempted Code

awk '{s[NR-1]=$1} END{print s[int(0.05-0.99)]}' input

Expected Output

99th    34.5
97th    34.4
95th    34.3
90th    34.2
80th    33.9
70th    33.4
60th    32.8
50th    32.2
40th    32.0
30th    31.9
20th    31.5
10th    31.0
5th     30.7

Answer 1

For calculation of percentile based on 5 values, one need to create a mapping between percentiles, and to interpolate between them. A process called 'Piecewise Linear function' (a.k.a. pwlf).

F(100) = 34.5 F(75) = 33.7 F(50) = 32.2 F(25) = 31.8 F(0) = 30.4

Mapping of any other x in the range 0..100, require linear interpolation betweeh F(L), and F(H) - where L is the highest value >= x, and H=L+1.

awk '
#! /bin/env awk
  # PWLF Interpolation function, take a value, and two arrays for X & Y
function pwlf(x, px, py) {
  # Shortcut to calculate low index of X, >= p
  p_l = 1+int(x/25)
  p_h = p_l+1
  x_l = px[p_l]
  x_h = px[p_h]
  y_l = py[p_l]
  y_h = py[p_h]
#print "X=", x, p_l, p_h, x_l, x_h, y_l, y_h
  return y_l+(y_h-y_l)*(x-x_l)/(x_h-x_l)
}

  # Read f Input in yy array, setup xx
{ yy[n*25] = $1  ; n++ }

  # Print the table
END {
  # Sort values of yy
  ny = asort(yy) ;
  # Create xx array 0, 25, ..., 100
  for (i=1 ; i<=ny ; i++) xx[i]=25*(i-1)

  # Prepare list of requested results
  ns = split("99 97 95 90 80 70 60 50 40 30 20 10 5", pv)
  for (i=1 ; i<=ns ; i++) printf "%dth %.1f\n",  pv[i], pwlf(pv[i], xx, yy) ;
}
' input

Technically a bash script, but based on comments to OP, better to place the whole think into script.awk, and execute as one lines. Solution has the '#!' to invoke awk script.

/path/to/script.awk < input