The HPBIN Procedure

Computing the Quantiles (Percentiles)

PROC HPBIN computes the 0% (minimum), 1%, 5%, 10%, 25%, 50%, 75%, 90%, 95%, 99%, and 100% (maximum) percentiles of each binning variable.

Let m be the number of nonmissing values for a variable, and let $x_1$, $x_2$, …, $x_ m$ represent the ordered values of the variable. Let the tth percentile be y, set $p = \frac{t}{100}$, and let $mp$ = j + g, where j is the integer part of $mp$ and g is the fractional part of $mp$. Then the tth percentile is described as:

\[ y = \begin{cases} x_ j & \text { if } g = 0 \\ x_{j+1} & \text { if } g > 0 \end{cases} \]

Note: To avoid the time-consuming sorting process, the HPBIN procedure uses an iterative projection method to compute percentiles according to the preceding formula.