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The data in the following table (Exercise 12.12) shows samples of size n = 20 drawn from four di?erent populations postulated to be normal, N , lognormal L, gamma G, and inverse gamma I, respectively.
XN
9.3745
XL
7.9128
XG
10.0896
XI
0.084029
8.8632
5.9166
15.7336
0.174586
11.4943
4.5327
15.0422
0.130492
9.5733
33.2631
5.5482
0.115567
9.1542
24.1327
18.0393
0.187260
9.0992
5.4151
17.9543
0.100054
10.2631
16.9556
12.5549
0.101405
9.8737
3.9345
9.6640
0.100835
7.8192
35.0376
14.2975
0.097173
10.4691
25.1182
4.2599
0.141233
9.6981
1.1804
19.1084
0.060470
10.5911
2.3503
7.0735
0.127663
11.6526
15.6894
7.6392
0.074183
10.4502
5.8929
14.1899
0.086606
10.0772
8.0254
13.8996
0.084915
10.2932
16.1482
9.7680
0.242657
11.7755
0.6848
8.5779
0.052291
9.3790
6.6974
7.5486
0.116172
9.9202
3.6909
10.4043
0.084339
10.9067
34.2152
14.8254
0.205748
(i) Validate these postulates using the full data sets. Note that the population parameters have not been speci?ed.
(ii) Using only the top half of each data set, repeat (i). For this particular example, what effect, if any, does sample size have on the probability plots approach to probability model validation?
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