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The distribution of rate of turn is unimodal with a strong positive skew (skewness = 4.1).
Figure 1 displays the distribution of rate of change in LTL among participants.
We found that the distribution of rate of change was normal over 2 years, and also at 4.5 years [ 10].
Author's response: Here, we cannot agree: we do not assume that the distribution of rate of evolution across sites, q v), is narrow.
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Estimates of the true mean rates incorporate information from a facility's observed rate with information from the distribution of rates of all facilities.
The distribution of rates of change in eGFR among subjects (the random effects) were depicted using Kernel-smoothed density estimates (15).
We assume that Nm(x) ~Gamma x, pm, αm), and similarly Nf(x) ~Gamma x, pf, αf), because of the long tailed distribution of the gamma function, reflecting known characteristics of the distribution of rates of partner change[ 28].
Real protein sequences also show rate heterogeneity across positions (which is modeled by a gamma distribution of rates of amino acid substitution per site in statistical comparison with equal rates across sites), such that most positions evolve slowly but some evolve quite rapidly [ 17].
On the amino-acid data set, we used the WAG empirical model of evolution, estimating the proportion of invariant sites by maximising the likelihood, and assuming a gamma shape distribution of rates of substitution among sites with a value of 2 for the gamma parameter.
The difference in the distributions of rate of cognitive and motor changes per year between genetic groups was first evaluated non-parametrically using Mann-Whitney U-tests (two subgroups).
Data were partitioned by codon position and gamma distribution of rate variation with a proportion of invariable sites was used.
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