mindist {DiceDesign}

Mindist measure

Description

Compute the mindist criterion (also called maximin)

Usage

mindist(design)

Arguments

design

a matrix (or a data.frame) representing the design of experiments in the unit cube [0,1]^d. If this last condition is not fulfilled, a transformation into [0,1]^{d} is applied before the computation of the criteria.

Details

The mindist criterion is defined by

mindist= \min_{x_{i}\in X} \left( \gamma_{i} \right)

where \gamma_{i} is the minimal distance between the point x_{i} and the other points x_{k} of the design.

A higher value corresponds to a more regular scaterring of design points.

Value

A real number equal to the value of the mindist criterion for the design.

Author(s)

J. Franco

References

Gunzburer M., Burkdart J. (2004), Uniformity measures for point samples in hypercubes, https://people.sc.fsu.edu/~jburkardt/.

Jonshon M.E., Moore L.M. and Ylvisaker D. (1990), Minmax and maximin distance designs, J. of Statis. Planning and Inference, 26, 131-148.

Chen V.C.P., Tsui K.L., Barton R.R. and Allen J.K. (2003), A review of design and modeling in computer experiments, Handbook of Statistics, 22, 231-261.

See Also

other distance criteria like meshRatio and phiP, discrepancy measures provided by discrepancyCriteria.

Examples

dimension <- 2
n <- 40
X <- matrix(runif(n*dimension), n, dimension)
mindist(X)