coverage {DiceDesign} | R Documentation |

## Coverage

### Description

Compute the coverage measure

### Usage

`coverage(design)`

### Arguments

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

### Details

The coverage criterion is defined by

```
coverage=\frac{1}{\bar{\gamma}} \left[ \frac{1}{n} \sum_{i=1}^{n}
\left( \gamma_{i} - \bar{\gamma} \right)^2 \right]^{1/2}
```

where `\gamma_{i}`

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

and the other points of the `design`

and `\bar{\gamma}`

is
the mean of the `\gamma_{i}`

.

Note that for a regular mesh, `cov`

=0. Then, a small value of `cov`

means that the design is close to a regular grid.

### Value

A real number equal to the value of the coverage 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/.

### 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)
coverage(X)
```

*DiceDesign*version 1.10 Index]