Investigating Variability by Simulation

The SIM2D Procedure

Investigating Variability by Simulation

The variability of Z(s), modeled by

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

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 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

Chapter Contents
Previous
Next
Top