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 The SIM2D Procedure

## Investigating Variability by Simulation

The variability of Z(s), modeled by

with the Gaussian covariance structure Cz(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 south-west point of the region and a point towards the north-east 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)

 X-coordinate of the grid point=0 Y-coordinate 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)

 X-coordinate of the grid point=75 Y-coordinate of the grid point=75

 Moments N 5000 Sum Weights 5000 Mean 40.1386868 Sum Observations 200693.434 Std Deviation 0.00250643 Variance 6.2822E-6 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 6.2822E-6 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

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