DiceDesign (version 1.10)

lhsDesign: Latin Hypercube Designs

Description

Simple (random) Latin Hypercube Design (randomized or centered) with \(n\) experiments in [0,1]\(^d\).

Usage

lhsDesign(n, dimension, randomized=TRUE, seed=NULL)

Value

A list with components:

n

the number of points

dimension

the number of variables

design

the design of experiments

randomized

the type of LHD

seed

the value of the seed

Arguments

n

number of experiments

dimension

number of variables

randomized

TRUE for randomized LHS; FALSE for centered LHS

seed

seed used to generate the random permutations and perturbations

Author

B. Iooss

Details

This program builds a Latin Hypercube Design (LHD), also called a Latin Hypercube Sample (LHS), on the space [0,1]\(^d\) (with uniform probability measures). LHD aims at ensuring that each variable has its whole range well scanned: the range of each variable is divided into \(n\) equally probable stratas. Each stratum of each variable contains only one point of the LHD. Centered LHD is obtained by choosing for each point the center of the corresponding case, while randomized LHD is obtained by adding random perturbations inside each point case.

Once the sample is generated, the uniform sample from a column can be transformed to any distribution by using the quantile functions.

References

McKay M., Conover W. and Beckman R. (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21, 2, 239-245.

Stein M. (1987) Large sample properties of simulations using Latin hypercube sampling, Technometrics, 29, 143-151.

See Also

LHD optimization (maximinSA_LHS,discrepSA_LHS,maximinESE_LHS ,discrepESE_LHS)

Examples

n <- 20
dimension <- 2
out <- lhsDesign(n, dimension)
out$design

## Change the dimnames, adjust to range (-10, 10) and round to 2 digits
xDRDN(out, letter = "T", dgts = 2, range = c(-10, 10))