Investigating Variability by Simulation
The variability of Z(s), modeled by
with the Gaussian covariance structure C_{z}(h) found
previously is not obvious from the covariance model form and
parameters. The variation around the mean of the surface
is relatively small, making it difficult visually to pick up
differences in surface plots of simulated realizations.
Instead, you investigate variations at selected grid points.
To do this investigation, this example uses PROC SIM2D and specifies the Gaussian
model with the parameters found previously. Five thousand simulations
(iterations) are performed on two points: the extreme southwest
point of the region and a point towards the northeast corner
of the region. Because of
the irregular nature of these points, a GDATA= data set
is produced with the coordinates of the selected points.
Summary statistics are computed for each of these grid points
by using a BY statement in PROC UNIVARIATE.
data grid;
input xc yc;
datalines;
0 0
75 75
run;
proc sim2d data=thick outsim=sim1;
simulate var=thick numreal=5000 seed=79931
scale=7.5 range=30.0 form=gauss;
mean 40.14;
coordinates xc=east yc=north;
grid gdata=grid xc=xc yc=yc;
run;
proc sort data=sim1;
by gxc gyc;
run;
proc univariate data=sim1;
var svalue;
by gxc gyc;
title 'Simulation Statistics at Selected Grid Points';
run;
Simulation Statistics at Selected Grid Points 
The UNIVARIATE Procedure 
Variable: SVALUE (Simulated Value at Grid Point) 
Xcoordinate of the grid point=0 Ycoordinate of the grid point=0 
Moments 
N 
5000 
Sum Weights 
5000 
Mean 
40.1387121 
Sum Observations 
200693.561 
Std Deviation 
0.54603592 
Variance 
0.29815523 
Skewness 
0.0217334 
Kurtosis 
0.0519914 
Uncorrected SS 
8057071.54 
Corrected SS 
1490.478 
Coeff Variation 
1.36037231 
Std Error Mean 
0.00772211 
Basic Statistical Measures 
Location 
Variability 
Mean 
40.13871 
Std Deviation 
0.54604 
Median 
40.14620 
Variance 
0.29816 
Mode 
. 
Range 
3.81973 


Interquartile Range 
0.76236 
Tests for Location: Mu0=0 
Test 
Statistic 
p Value 
Student's t 
t 
5197.892 
Pr > t 
<.0001 
Sign 
M 
2500 
Pr >= M 
<.0001 
Signed Rank 
S 
6251250 
Pr >= S 
<.0001 
Quantiles (Definition 5) 
Quantile 
Estimate 
100% Max 
41.9369 
99% 
41.4002 
95% 
41.0273 
90% 
40.8334 
75% Q3 
40.5168 
50% Median 
40.1462 
25% Q1 
39.7544 
10% 
39.4509 
5% 
39.2384 
1% 
38.8656 
0% Min 
38.1172 
Extreme Observations 
Lowest 
Highest 
Value 
Obs 
Value 
Obs 
38.1172 
2691 
41.8085 
1149 
38.2959 
1817 
41.8251 
3612 
38.3370 
3026 
41.8446 
3757 
38.3834 
2275 
41.9338 
135 
38.4198 
3100 
41.9369 
4536 
Simulation Statistics at Selected Grid Points 
The UNIVARIATE Procedure 
Variable: SVALUE (Simulated Value at Grid Point) 
Xcoordinate of the grid point=75 Ycoordinate of the grid point=75 
Moments 
N 
5000 
Sum Weights 
5000 
Mean 
40.1386868 
Sum Observations 
200693.434 
Std Deviation 
0.00250643 
Variance 
6.2822E6 
Skewness 
0.00937779 
Kurtosis 
0.0088601 
Uncorrected SS 
8055570.91 
Corrected SS 
0.03140472 
Coeff Variation 
0.00624443 
Std Error Mean 
0.00003545 
Basic Statistical Measures 
Location 
Variability 
Mean 
40.13869 
Std Deviation 
0.00251 
Median 
40.13870 
Variance 
6.2822E6 
Mode 
. 
Range 
0.01756 


Interquartile Range 
0.00346 
Tests for Location: Mu0=0 
Test 
Statistic 
p Value 
Student's t 
t 
1132380 
Pr > t 
<.0001 
Sign 
M 
2500 
Pr >= M 
<.0001 
Signed Rank 
S 
6251250 
Pr >= S 
<.0001 
Quantiles (Definition 5) 
Quantile 
Estimate 
100% Max 
40.1468 
99% 
40.1445 
95% 
40.1428 
90% 
40.1419 
75% Q3 
40.1404 
50% Median 
40.1387 
25% Q1 
40.1369 
10% 
40.1355 
5% 
40.1346 
1% 
40.1328 
0% Min 
40.1293 
Extreme Observations 
Lowest 
Highest 
Value 
Obs 
Value 
Obs 
40.1293 
2176 
40.1465 
1278 
40.1299 
1262 
40.1465 
3980 
40.1302 
2383 
40.1468 
676 
40.1306 
2156 
40.1468 
1514 
40.1308 
643 
40.1468 
329 

Figure 58.3: Simulation Statistics at Selected Grid Points
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.