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For these simulations, the two data sets were generated from the same distribution, so that we would expect the test to not result in rejection of the null hypothesis.
The motivation of employing Student's t distribution is that the Cauchy and Gaussian distributions are a part of the α-stable distribution family [41], which has a stable property of a random variable, namely, a linear combination of two independent random variables generated from the same distribution family also has the same distribution up to location and scale parameters.
Noise peaks were generated from the same distribution as the discriminating peaks but with the means of the two disease groups being equal.
In a simulated data set, 20 gene expression profiles of length 6000 were randomly generated from the same distribution.
The kolmogorov-smirnov test [ 10] was used to determine the probability that two lists of ORRs were generated from the same distribution.
(The y*'s and x*'s have been generated from the same distribution except that the distribution of the y*'s is shifted δ units to the right).
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The homogeneity test becomes a problem of testing whether two samples of random variables are generated from the same distribution., the unbiased empirical estimation of the MMD is defined as follows.
However, the differences are not significant and our permutation test results suggest that we cannot reject the null hypothesis - i.e., the differences within all groups can potentially be generated from the same underlying distribution.
Although NB is based on the assumption of independence between predictors, a good performance has been shown for functional dependencies, that is, predictors that are generated from the same underlying distribution [65].
The expression intensities of DR genes for cases are generated from the same Gamma distribution as UR genes in the same study, but with a negative sign.
Our method is based on the maximum mean discrepancy (MMD), a recent technique from the machine learning literature, which tests whether two samples have been generated from the same probability distribution (Gretton et al., 2007, 2012).
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