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Copulas are functions developed by Sklar (1959 , 1996 that describe dependencies among random variables by linking a joint multidimensional distribution to its one-dimensional margins.
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Among other space filling designs we especially investigate the very efficient Latin Hypercube Design in terms of its capability to represent a multidimensional distribution with its experiments.
On the example of the multivariate normal distribution we demonstrate that our Depth-Design represents a multidimensional distribution with much less experiments in comparison to the Latin Hypercube design.
A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate.
First, we explore this domain by Latin Hypercube (LH) sampling, as described in detail in the Additional file 3. (LH sampling is commonly used to generate multidimensional samples from a multidimensional distribution [ 17]).
A recently developed algorithm is used to invert the data and extract stable multidimensional distribution functions in an efficient manner.
We demonstrate the quantitative extraction of multidimensional distribution functions in the presence of grossly inhomogeneous fields.
The distinct conditional distributions are called latent profiles, and these are normally characterized by their conditional means on the dimensions of the multidimensional distribution and by the percentage of students forming the profiles.
However, such approach would fail for more complex classification problems when a multidimensional distribution of positive or negative outcomes is not the direct product of corresponding one-dimensional distributions.
One of the most used MC method is the Latin Hypercube Sampling (LHS), which is a stratified sampling without replacement technique that generates sets of parameter values from a multidimensional distribution [ 25, 26].
One strength of the approach, which used direct fitting of the multidimensional distribution data from the National Health and Nutritional Examination Survey III, was that it allowed for a comprehensive validation of the simulated population's multivariate diversity, including the correlation of clinical measures.
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