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Table 2 Empirical fittings of the completeness of trajectories. Fitting quality of six standard long-tailed distributions to the empirical PDF of trajectory completeness, in terms of \(R^{2}\) and \(D_{\mathrm{KS}}\). Rows refer to different combinations of observation period \(\mathcal{T}\) and time resolution τ. Best-fit \(R^{2}\) and \(D_{\mathrm{KS}}\) are highlighted in bold

From: Complete trajectory reconstruction from sparse mobile phone data

Duration \(\mathcal{T}\) Resolution τ Weibull Lognormal Gamma Pareto Levy Power law
\(D_{\mathrm{KS}}\) \(R^{2}\) \(D_{\mathrm{KS}}\) \(R^{2}\) \(D_{\mathrm{KS}}\) \(R^{2}\) \(D_{\mathrm{KS}}\) \(R^{2}\) \(D_{\mathrm{KS}}\) \(R^{2}\) \(D_{\mathrm{KS}}\) \(R^{2}\)
7 d 15 min 0.0334 0.9990 0.0318 0.9973 0.3710 0.4679 0.0495 0.9969 0.2509 0.8046 0.3538 0.5031
30 min 0.0302 0.9993 0.0345 0.9967 0.0548 0.9962 0.1716 0.8973 0.2649 0.7848 0.3587 0.4894
60 min 0.0278 0.9990 0.0372 0.9958 0.0475 0.9977 0.1198 0.9516 0.2888 0.7506 0.4162 0.2041
120 min 0.0375 0.9972 0.0443 0.9938 0.0629 0.9853 0.1043 0.9768 0.3238 0.6977 0.2456 0.7450
15 d 15 min 0.0264 0.9986 0.0233 0.9984 0.3594 0.5007 0.0627 0.9893 0.2620 0.7853 0.3949 0.4120
30 min 0.0208 0.9995 0.0264 0.9980 0.0271 0.9991 0.0724 0.9851 0.2765 0.7647 0.3576 0.4975
60 min 0.0188 0.9997 0.0279 0.9974 0.0257 0.9987 0.0935 0.9719 0.2997 0.7315 0.3176 0.6076
120 min 0.0254 0.9987 0.0332 0.9961 0.0913 0.9572 0.1880 0.8780 0.3349 0.6792 0.2721 0.7116
30 d 15 min 0.0239 0.9985 0.0207 0.9985 0.3514 0.5261 0.0700 0.9835 0.2619 0.7872 0.3829 0.4365
30 min 0.0205 0.9992 0.0216 0.9983 0.0203 0.9991 0.1528 0.8976 0.2763 0.7661 0.3912 0.4149
60 min 0.0149 0.9996 0.0263 0.9975 0.0289 0.9982 0.0895 0.9702 0.3003 0.7346 0.3131 0.6212
120 min 0.0239 0.9984 0.0315 0.9962 0.0995 0.9479 0.1069 0.9538 0.3337 0.6893 0.3154 0.6176
60 d 15 min 0.0266 0.9980 0.0239 0.9977 0.1990 0.8284 0.0458 0.9934 0.2527 0.8076 0.3850 0.4156
30 min 0.0233 0.9985 0.0234 0.9976 0.0286 0.9974 0.1944 0.8669 0.2649 0.7903 0.3897 0.4212
60 min 0.0207 0.9985 0.0264 0.9970 0.0310 0.9980 0.0772 0.9769 0.2883 0.7622 0.3451 0.5635
120 min 0.0245 0.9975 0.0316 0.9958 0.0754 0.9750 0.0946 0.9617 0.3209 0.7196 0.3491 0.5070
90 d 15 min 0.0298 0.9954 0.0329 0.9954 0.3619 0.5248 0.0322 0.9954 0.2371 0.8390 0.3866 0.4528
30 min 0.0336 0.9958 0.0335 0.9950 0.0583 0.9864 0.0398 0.9942 0.2487 0.8264 0.3819 0.4774
60 min 0.0305 0.9960 0.0355 0.9944 0.0454 0.9913 0.0611 0.9843 0.2705 0.8020 0.3231 0.6123
120 min 0.0369 0.9940 0.0379 0.9932 0.0486 0.9927 0.0760 0.9743 0.2998 0.7687 0.3359 0.5885