### Table 2: Tail distribution for n=5

"... In PAGE 9: ... But for smaller vertex numbers these values can be listed to give a sense of the sparseness of the tail. Table2 lists all of the values in the tail of the distribution for n=5 vertices for class sizes greater than 24 along with their distribution percentages, while Table 3 does the same for n=6. For both n=5 and n=6, the distribution of classes of size 24 or smaller is very similar to that of Figure 3 with 99.... ..."

### Table 3: Tail distribution for n=6

"... In PAGE 9: ... But for smaller vertex numbers these values can be listed to give a sense of the sparseness of the tail. Table 2 lists all of the values in the tail of the distribution for n=5 vertices for class sizes greater than 24 along with their distribution percentages, while Table3 does the same for n=6. For both n=5 and n=6, the distribution of classes of size 24 or smaller is very similar to that of Figure 3 with 99.... ..."

### Table 4. Tail Weight and Asymmetry for All Distributions

1989

"... In PAGE 8: ...6% extremely or exponentially asymmetric). 35 Crossing the values for tail weight and symmetry, Table4 shows that 30 (6.8%) of the 440 distributions exhibit both tail weight and symmetry approximating that expected at the Gaussian and that 21 (48%) exhibited relative symmetry and tail weights lighter than that expected at the Gaussian.... In PAGE 11: ...1%) would qualify for the title.1 50 Table4 shows that most cells of the tail weight/asymmetry matrix are filled and that counts in each cell tend to remain fairly constant as one moves from light tails to heavy tails or from relative symmetry to extreme asymmetry. Table 4 also shows the poor match between real data and the smooth mathematical functions generally applied in Monte Carlo robustness studies.... In PAGE 11: ...1 50 Table 4 shows that most cells of the tail weight/asymmetry matrix are filled and that counts in each cell tend to remain fairly constant as one moves from light tails to heavy tails or from relative symmetry to extreme asymmetry. Table4 also shows the poor match between real data and the smooth mathematical functions generally applied in Monte Carlo robustness studies. Distributions exhibiting either extremely heavy tail weights (exponential) or extremely light tail weights (uniform) tend also to be asymmetric.... ..."

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### Table 6. Tail Weight and Asymmetry for Psychometric Distributions

1989

"... In PAGE 9: ...7%) exhibiting relative symmetry and tail weights less than that expected at the Gaus- sian. 37 Table6 shows that 4 psychometric distributions (3.2%) exhibited both relative symmetry and tail weights near the Gauss ian and 39 distributions (3 1.... In PAGE 16: ...xtremely conservative, having an obtained alpha of about .01 when nominal alpha was .05. Unfortu- nately, this population was not included in their discussion of power. However, from their Table6 , it is interesting to note that the only comparison between two-sample tests in which a substantial power advantage accrues to any test is that between populations IIIA and IA (uniform). In that situation, the van der Waerden test exhibited a considerable power advantage at sample size 10 over both the parametric confidence interval and the Mann-Whitney/Wilcoxon tests.... ..."

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### Table 1: Summary of Performance of -estimator on heavy-tailed distributions (250 trials each case).

1999

"... In PAGE 13: ... 3 Empirical Evaluation This section presents the results of applying the algorithm shown in Figure 4 to a variety of synthetic datasets. Table1 shows a summary of the results of applying the algorithm to datasets drawn from a variety of heavy-tailed distributions: the Pareto distribution (de ned in Section 2.2) with k = 1 and = 0.... In PAGE 15: ...1 of the true value, regardless of the particular value of . An important feature of the estimator evident from Figures 10, 9, and Table1 is that both bias and variance decrease with increasing sample size. This feature makes it especially attractive for use on datasets taken from computing and telecommunications systems, where large sample sizes are common.... ..."

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### Table 2: Summary of Performance of -estimator on non-heavy-tailed distributions (250 trials each case).

1999

"... In PAGE 13: ... As approaches 2, the estimator shows some downward bias. Table2 shows the performance of the estimator when applied to datasets drawn from a variety of non-heavy-tailed distributions. Again, each row corresponds to the results of 250 trials, and the \% Estimates quot; column counts the percent of times the estimator returned a value.... In PAGE 13: ... Again, each row corresponds to the results of 250 trials, and the \% Estimates quot; column counts the percent of times the estimator returned a value. The rst two sections of Table2 show the estimator apos;s performance on Normal distributions with unit variance and the exponential distribution with CDF P [X x] = 1 ? e? x for = 1. This shows that nite-variance distributions, which tend to Normal when aggregated, can show scaling behavior with close to 2.... In PAGE 13: ... This shows that nite-variance distributions, which tend to Normal when aggregated, can show scaling behavior with close to 2. The next two sections of Table2 shows the estimator apos;s performance on the Lognormal distri- bution: X = e Z where Z N( ; ). For these distributions (the mean of ln X) was 0 and (the standard deviation of ln X) was either 1 or 2.... In PAGE 13: ... Note that when = 2 the estimator cannot distinguish the asymptotically Normal scaling taking place from heavy-tailed scaling. The nal section of Table2 shows the estimator apos;s performance on the Weibull distribution with CDF P [X x] = 1 ? exp(?(x=a))b. In these tests a = 1 and b = e?1.... ..."

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### Table 5. Tail Weight and Asymmetry for Ability Distributions

1989

"... In PAGE 9: ...36 [page 161] Table5 shows that results were similar for ability measures, with 23 (10.0%) at or about the Gaussian and 20 (8.... In PAGE 11: ...6% had at least one moderately heavy tail) than did ability measures. 49 Table5 suggests that general ability measures tend to exhibit less extreme contamination than do the other measures. None had tail weights at or near the uniform, and only 3.... ..."

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### Table 6 shows the results of the T-test with two-tailed distribution conducted on unit price

"... In PAGE 9: .................... 37 Table6 : T-test values for large customers .... ..."

### Table 2: Weight distributions of tail{biting codes

1998

"... In PAGE 5: ... 6 is achieved, although we in- creased the complexity of the tail{biting component code by a factor of 4. This result becomes under- standable if we consider the weight distributions of C13 D and C12 E ( Table2 ). Both encoders map weight{ one information vectors to parity weight eight and weight{two information vectors to parity weight four (at least).... ..."

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