Percentile Definitions

You can use the PCTLDEF= option to specify one of five definitions for computing quantile statistics (percentiles). Suppose that is the number of nonmissing values for a variable and that represent the ordered values of the analysis variable. For the tth percentile, set .

For the following definitions numbered 1, 2, 3, and 5, express as

     

where is the integer part of , and is the fractional part of . For definition 4, let

     

The tth percentile (call it ) can be defined as follows:

PCTLDEF=1

weighted average at

     

where is taken to be .

PCTLDEF=2

observation numbered closest to

     

where is the integer part of if . If , then if is even, or if is odd.

PCTLDEF=3

empirical distribution function

     
     
PCTLDEF=4

weighted average aimed at

     

where is taken to be .

PCTLDEF=5

empirical distribution function with averaging