We present a systematic study of the dynamical scaling process leading to the establishment of the Kolmogorov-Zakharov (KZ) spectrum in weak three-wave turbulence. In the finite-capacity case, in which the transient spectrum reaches infinite frequency in finite time, the dynamical scaling exponent is anomalous in the sense that it cannot be determined from dimensional considerations. As a conse...

1 Some Basic Theory 1 1.1 Consistency and Unbiasedness at a Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Kolmogorov–Smirnov Statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Order Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Proof of the Kolmogorov–Smirnov Theorem . . ....

The concepts of cumulative distribution function and empirical distribution function are investigated for fuzzy random variables. Some limit theorems related to such functions are established. As an application of the obtained results, a method of handling fuzziness upon the usual method of Kolmogorov–Smirnov one-sample test is proposed. We transact the α-level set of imprecise observations in ...

The methods measuring the departure between observation and the model were reviewed. The following statistics were applied on two experimental data sets: ChiSquared, Kolmogorov-Smirnov, Anderson-Darling, Wilks-Shapiro, and Jarque-Bera. Both investigated sets proved not to be normal distributed. The Grubbs’ test identified one outlier and after its removal the normality of the set of 205 chemica...

The use of the Kolmogorov-Smirnov (KS) statistic for testing hypotheses regarding activation in blood oxygenation level-dependent functional MRI data is critiqued on both theoretical and empirical grounds. Theoretically, it is argued that the KS test is formally unable to support inferences of interest to most neuro-imaging studies and has reduced sensitivity compared with parametric alternativ...