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Table 4 Model selection and validation from two goodness-of-fit tests: the maximum log-likelihood criterion (ln L) and the Kolmogorov-Smirnov (K-S) minimum distance criterion

From: Earthquake interevent time distribution in Kachchh, Northwestern India

  Maximum likelihood K-S min. distance
Distribution ln L AIC K-S distancea
Exponential −50.2774 102.5549 0.1228 (15.8136)
Gamma −50.02s05 104.0411 0.1227 (06.9809)
Lognormal −50.3935 104.7871 0.1495 (15.8136)
Weibull −49.9635 103.9271 0.1505 (06.9809)
Levy −53.9911 109.9821 0.1709 (20.0959)
Maxwell −59.9866 121.9731 0.2819 (06.9809)
Pareto −54.1220 112.2439 0.3488 (06.9809)
Rayleigh −53.6749 109.3498 0.3055 (05.1123)
Inverse Gaussian −50.6296 105.2592 0.1790 (15.8136)
Inverse Weibull −51.8923 107.7907 0.1496 (05.1123)
Exponentiated exponential −49.9800 103.9601 0.1406 (06.9809)
Exponentiated Rayleigh −49.9891 103.9783 0.1714 (06.9809)
Exponentiated Weibull −49.9611 105.9223 0.1549 (06.9809)
  1. ln L – log-likelihood value, AIC – value of Akaike information criterion
  2. aNumber in parenthesis is the abscissa value, where K-S distance is achieved