Percentile Definitions

BOXCHART Statement

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 x₁, x₂, ... ,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 x₀ is taken to be x₁.

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

$y=x_{j} & {if } \, g=0 \y=x_{j+1} & {if } \, g \gt 0 \$

PCTLDEF=4

This uses the weighted average aimed at x_p(n+1)

y=(1-g)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

$y=(x_{j} + x_{j+1})/2 & {if } \, g = 0 \y=x_{j+1} & {if } \, g \gt 0 \$

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