mindist: Mindist measure In DiceDesign: Designs of Computer Experiments

Description

Compute the `mindist` criterion (also called maximin)

Usage

 `1` ```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 (g_1, ... g_n)

where g_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`.

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.

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

Examples

 ```1 2 3 4``` ```dimension <- 2 n <- 40 X <- matrix(runif(n*dimension), n, dimension) mindist(X) ```

Example output

```[1] 0.01543376
```

DiceDesign documentation built on Feb. 13, 2021, 1:06 a.m.