Random Latin Hypercube
Draws a Latin Hypercube Sample from a set of uniform distributions for use in creating a Latin Hypercube Design. This sample is taken in a random manner without regard to optimization.
randomLHS(n, k, preserveDraw)
The number of partitions (simulations or design points)
The number of replications (variables)
Default:FALSE. Ensures that two subsequent draws
with the same
Latin hypercube sampling (LHS) was developed to generate a distribution
of collections of parameter values from a multidimensional distribution.
A square grid containing possible sample points is a Latin square iff there
is only one sample in each row and each column. A Latin hypercube is the
generalisation of this concept to an arbitrary number of dimensions. When
sampling a function of
k variables, the range of each variable is divided
n equally probable intervals.
n sample points are then drawn such that a
Latin Hypercube is created. Latin Hypercube sampling generates more efficient
estimates of desired parameters than simple Monte Carlo sampling.
This program generates a Latin Hypercube Sample by creating random permutations
of the first
n integers in each of
k columns and then transforming those
integers into n sections of a standard uniform distribution. Random values are
then sampled from within each of the n sections. Once the sample is generated,
the uniform sample from a column can be transformed to any distribution by
using the quantile functions, e.g. qnorm(). Different columns can have
k Latin Hypercube Sample matrix with values uniformly distributed on [0,1]
Rob Carnell and D. Mooney
Stein, M. (1987) Large Sample Properties of Simulations Using Latin Hypercube Sampling. Technometrics. 29, 143–151.
optimumLHS to generate Latin Hypercube Samples.
augmentLHS to modify and augment existing designs.
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# draw a Latin hypercube randomLHS(4, 3) # transform a Latin hypercube X <- randomLHS(5, 2) Y <- matrix(0, nrow=5, ncol=2) Y[,1] <- qnorm(X[,1], mean=3, sd=0.1) Y[,2] <- qbeta(X[,2], shape1=2, shape2=3) # check the preserveDraw option set.seed(1976) X <- randomLHS(6,3,preserveDraw=TRUE) set.seed(1976) Y <- randomLHS(6,5,preserveDraw=TRUE) all(abs(X - Y[,1:3]) < 1E-12) # TRUE
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