Figure 1

A first example of the proposed test, with $N=64$ i.i.d. RVs drawn from a Gaussian with unit variance (squares) and a symmetric Lévy distribution $L_{\mu }(x)$ with $\mu =1.3$ (circles). Inset: Comparing the cumulative distribution function $F(x)$ (lines) to its empirical estimate from the 64 data points shows that one distribution is broader than the other but does not allow for a clear distinction between the two data sets. Main plot: This difference is, however, clearly seen under application of the record-based test for subsamples of size $n=16$. Dotted and dash-dotted lines show the prediction for $l_{16,15}(c)$ for independent RV’s.Reuse & Permissions

Figure 2

Sample-to-sample fluctuations of the HTI ${\widehat{l}}_{n,n-1}$ for different distributions. Lines show mean values of the correlation $l_{16,15}(c)$ obtained from simulations of independent RV’s (labeled exact), symbols show the mean value of the HTI and error bars indicate the standard deviation of the fluctuations for the symmetric Lévy-stable distribution with tail parameter $\mu =1.3$ and uniform distribution on (0,1) (top), and the Pareto distribution with $\mu =2.0$ and standard normal distribution (bottom). The HTI was obtained from simulations with internal statistics $s={10}^4$ (Pareto) or $s={10}^5$ (all other) and averaged over $S={10}^3$ independent data sets. Insets show how the correlations at the value $c^{*}=0.25$, where correlations deviate maximally from unity, grow as a function of $n$ while keeping $N$ fixed.Reuse & Permissions

Figure 3

Magnitude of sample-to-sample fluctuations for three of the cases considered in Fig. 2. With increasing internal statistics $s$, the sample-to-sample fluctuations decrease to a limiting value (main plot). This limiting value increases with $n/N$ (inset), indicating that best results in terms of fluctuations are obtained by considering short subsequences. In the main plot, $N=64$ and $n=16$.Reuse & Permissions

Figure 4

Top: Three randomly chosen subsets of length $N=64$ each from the ISI citation data set [6]. The HTI was computed with internal statistics $s={10}^6$ and $n=16$. The main plot shows attractive correlations in all three cases, the inset verifies growth of these correlations with $n$. Bottom: Removing the largest and even the top two entries of data set 2 does not change the result of the test. In data set 3, which is a somewhat extreme case in that the largest value is more than a factor 10 greater than the second largest, the correlations remain attractive upon removal of the largest entry but the magnitude of correlations no longer increases with $n$.Reuse & Permissions