meshRatio {DiceDesign} | R Documentation |

## MeshRatio measure

### Description

The `meshRatio`

criterion is the ratio between the
maximimum and the minimum distance between two points of the experimental design.

### Usage

`meshRatio(design)`

### Arguments

`design` |
a matrix (or a data.frame) representing the design of experiments in the unit cube [0,1] |

### Details

The `meshRatio`

criterion is defined by

```
meshRatio=\frac{\max_{1\leq i \leq n} \gamma_{i}}{\min_{1\leq i \leq n}
\gamma_{i}}
```

where `\gamma_{i}`

denotes the minimal distance between the point
`x_{i}`

and the other points of the `design`

.

Note that for a regular mesh, `meshRatio`

=1.

### Value

A real number equal to the value of the meshRatio criterion for the `design`

.

### Author(s)

J. Franco

### References

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

### See Also

Other distance criteria like `meshRatio`

, `phiP`

and `mindist`

.

Discrepancy measures provided by `discrepancyCriteria`

.

### Examples

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

*DiceDesign*version 1.10 Index]