PROC SHEWHART: Percentile Definitions

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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 $\text{[math]}$ equal the number of nonmissing values for a variable, and let $\text{[math]}$ represent the ordered values of the process variable. For the $\text{[math]}$ th percentile, set $\text{[math]}$ , and express $\text{[math]}$ as

$\text{[math]}$

where $\text{[math]}$ is the integer part of $\text{[math]}$ , and $\text{[math]}$ is the fractional part of $\text{[math]}$ .

The $\text{[math]}$ th percentile (call it $\text{[math]}$ ) can be defined in five ways, as described in the next five sections.

PCTLDEF=1

This uses the weighted average at $\text{[math]}$

$\text{[math]}$

where $\text{[math]}$ is taken to be $\text{[math]}$ .

PCTLDEF=2

This uses the observation numbered closest to $\text{[math]}$

$\text{[math]}$

where $\text{[math]}$ is the integer part of $\text{[math]}$ .

PCTLDEF=3

This uses the empirical distribution function

$\text{[math]}$

PCTLDEF=4

This uses the weighted average aimed at $\text{[math]}$

$\text{[math]}$

where $\text{[math]}$ , and where $\text{[math]}$ is taken to be $\text{[math]}$ .

PCTLDEF=5

This uses the empirical distribution function with averaging

$\text{[math]}$

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