|
EMPIRICAL QUANTILE FUNCTIONName:
Given a set of ordered data, x1 ≤ x2 ... ≤ xn, an empirical estimate of the quantile function can be obtained from the following piecewise linear function
\( \frac{2j - 1}{2n} \le u \le \frac{2j + 1}{2n} \) This will be computed for a specified number of equi-spaced points between the lower and upper limits. Dataplot will use the number of points in the sample if this is greater than 1,000. Otherwise 1,000 points will be used.
<SUBSET/EXCEPT/FOR qualification> where <x> is the response variable; <y> is a variable containing the empirical quantile function; <u> is a variable containing the values where the empirical quantile function is computed; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET Y U = EMPIRICAL QUANTILE FUNCTION X SUBSET X > 0
Parzen (1983), "Informative Quantile Functions and Identification of Probability Distribution Types", Technical Report No. A-26, Texas A&M University.
. Step 1: Define some default plot control features . title offset 2 title case asis case asis label case asis line color blue red multiplot scale factor 2 multiplot corner coordinates 5 5 95 95 . . Step 2: Create 50, 100, 200, and 1000 normal random numbers and . compute the empirical quantile funciton . let nv = data 50 100 200 1000 let p = sequence 0.01 0.01 .99 let y2 = norppf(p) . . Step 3: Loop through the four cases and compute and plot the . empirical quantile funciton with overlaid NORPPF . multiplot 2 2 loop for k = 1 1 4 let n = nv(k) let x = norm rand numb for i = 1 1 n let y u = empirical quantile function x title N: ^n plot y u and plot y2 p end of loop end of multiplot . justification center move 50 97 text Empirical Quantile Functions (blue) Overlaid with ... NORPPF (red) for Normal Random Numbers move 50 5 text u direction vertical move 5 50 text Q(u)
|
Privacy
Policy/Security Notice
NIST is an agency of the U.S.
Commerce Department.
Date created: 07/20/2017 |