Percentile Definitions
You can use the PCTLDEF= option to specify one of five definitions for
computing quantile statistics (percentiles). Suppose that n equals
the number of nonmissing values for a variable and that x_{1}, x_{2}, ... ,x_{n} represents the ordered values of the analysis
variable. For the tth percentile, set p =t/100.
For the following definitions numbered 1, 2, 3, and 5, express np as

np = j + g
where j is the integer part of np, and g is the
fractional part of np. For definition 4, let

(n+1)p=j+g
The tth percentile (call it y) can be defined as follows:
 PCTLDEF=1
 weighted average at x_{np}

y = (1  g)x_{j} + gx_{j+1}
where x_{0} is taken to be x_{1}
 PCTLDEF=2
 observation numbered closest to np

y = x_{i}
where i is the integer part of np + 1/2
if . If g=1/2, then
y=x_{j} if j is even, or
y=x_{j+1} if j is odd.
 PCTLDEF=3
 empirical distribution function

y = x_{j} if g = 0

y = x_{j+1} if g > 0
 PCTLDEF=4
 weighted average aimed at x_{p(n+1)}

y=(1  g)x_{j} + gx_{j+1}
where x_{n+1} is taken to be x_{n}
 PCTLDEF=5
 empirical distribution function with averaging

y = (x_{j} + x_{j+1})/2 if g = 0

y = x_{j+1} if g > 0
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.