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In the second case, the histogram is modelled using a Gamma distribution function where the 90% cumulative interval provides the threshold.
We applied lumped parameter models using a gamma distribution to calculate the Mean Transit Time (MTT) of water over the entire period of record and to evaluate how inter-annual differences in transit times relate to hydroclimatic variability.
Trees were reconstructed by maximum likelihood using a gamma distribution with four rate categories and coefficients of variation (base frequencies, transition/transversion ratio, rates of change and gamma distribution shape parameter) estimated from the data using the DNAML programme.
NJ was performed in Mega 4 [29] using a gamma distribution of among site substitution rates (0.66, as estimated by PhyML), the Poisson correction model and 5000 bootstrap replicates.
Rate variation across sites was modeled using a gamma distribution.
A generalized linear model using a gamma distribution was used to control for these differences.
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For now, we use a Gamma distribution (Fig. 1) for p ϕ with mean ϕ 0 = 0.01.
Finally, in order to more directly illustrate how replay terminates after small patterns, we show a scatter plot of 104 sample pairs ( M τ, M τ + 1 ), where τ is the last time step at which the pattern was replayed with sufficient quality Γ τ > 0.5 (Fig. 9; note that here we again used a Gamma distribution to achieve comparability with Fig. 4).
For both models, we used a gamma distribution with six categories to account for rate variation among sites.
I use a Gamma distribution with mean Tg = 2.85 days and standard deviation 0.93 days, as reported in [30].
We used a gamma distribution because variances are always non-negative and gamma distributions have support only over the non-negative domain.
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