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The SHEWHART Procedure

Percentile Definitions

You can use the PCTLDEF= option to specify one of five definitions for computing quantile statistics (percentiles). Let equal the number of nonmissing values for a variable, and let represent the ordered values of the process variable. For the th percentile, set , and express as

     

where is the integer part of , and is the fractional part of .

The th percentile (call it ) can be defined in five ways, as described in the next five sections.

PCTLDEF=1

This uses the weighted average at

     

where is taken to be .

PCTLDEF=2

This uses the observation numbered closest to

     

where is the integer part of .

PCTLDEF=3

This uses the empirical distribution function

     

PCTLDEF=4

This uses the weighted average aimed at

     

where , and where is taken to be .

PCTLDEF=5

This uses the empirical distribution function with averaging

     
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