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The SIM2D Procedure

Investigating Variability by Simulation

The variability of Z(s), modeled by

Z(s) = \mu + \varepsilon(s)
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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