Percentile Definitions
You can use the PCTLDEF= option to
specify one of five definitions for computing quantile
statistics (percentiles).
Let n equal the number of nonmissing values for a
variable, and let x_{1}, x_{2}, ... ,x_{n} represent the ordered
values of the process variable. For the t^{ th} percentile, set p =t/100, and
express
np as

np = j + g
where j is the integer part of np, and
g is the fractional part of np.
The t^{ th} percentile (call it y)
can be defined in
five ways, as described in the next five sections.
PCTLDEF=1
This uses the weighted average at x_{np}

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

y=x_{i}
where i is the integer part of np + 1/2.
PCTLDEF=3
This uses the empirical distribution function
PCTLDEF=4
This uses the weighted average aimed at x_{p(n+1)}

y=(1g)x_{j} + gx_{j+1}
where (n+1)p=j+g, and
where x_{n+1} is taken to be x_{n}.
PCTLDEF=5
This uses the empirical
distribution function with averaging
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.