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As the COP approach has no closed-form solution, simulations from this multivariate distribution are necessary.
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Therefore, any multivariate distribution is applicable.
In other words, the multivariate distribution is coupled to its marginal distributions.
A multivariate generalization of classical order statistics for random samples from a continuous multivariate distribution was defined by Corley [18].
If a multivariate distribution is parametrically specified, often the lower-dimensional marginals follow the same distribution of an appropriate dimension.
However, in these studies, the moment test as a GOF test was applied to each dimension individually and the possible contribution of inter-dimensional dependency to the multivariate distribution was not considered.
The multivariate distribution of the present data does not meet these recommendations indicating the multivariate distribution is non-normal.
The multivariate distribution is used to model one variable for multiple tips on a tree, rather than to model multiple characters.
The crude assumption that the multivariate distribution is Gaussian is crucial in the derivation, whereas the unrealistic assumption that v j j ′ = 0 for j ≠ j ′ is made for simplicity.
In the articles listed earlier, a number of well-known multivariate distributions are shown to possess the END properties.
However, the multivariate normal distribution used to model the data would be difficult to replace by another one, because few continuous multivariate distributions are available (although for overdispersed data, one can use the heavy-tailed multivariate Student's t in place of the normal [ 33, p.446]).
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