# dw: Devroye-Wise estimator In alphahull: Generalization of the Convex Hull of a Sample of Points in the Plane

## Description

This function calculates the Devroye-Wise estimator of a given sample of points in the plane for ε>0.

## Usage

 `1` ```dw(x, y = NULL, eps) ```

## Arguments

 `x, y` The `x` and `y` arguments provide the `x` and `y` coordinates of a set of points. Alternatively, a single argument `x` can be provided, see Details. `eps` Value of ε.

## Details

An attempt is made to interpret the arguments x and y in a way suitable for computing the Devroye-Wise estimator. Any reasonable way of defining the coordinates is acceptable, see `xy.coords`.

## Value

Given a sample of points in the plane, the estimator is defined as union of balls of radius ε with centers in the sample points. For each arc in the boundary of the Devroye-Wise estimator, the columns of the output matrix store the center c and radius r of the arc, the unitary vector v, the angle θ that define the arc and the indices of the end points.

## References

Devroye, L. and Wise, G. (1980) Detection of abnormal behaviour via nonparametric estimation of the support. SIAM J. Appl. Math. 3, pp. 480-488.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```## Not run: # Uniform sample of size n = 200 in the annulus B(c, 0.5)\B(c, 0.25), # with c = (0.5, 0.5). n <- 200 theta <- runif(n, 0, 2*pi) r <- sqrt(runif(n, 0.25^2, 0.5^2)) x <- cbind(0.5 + r*cos(theta), 0.5 + r*sin(theta)) eps <- 0.05 dw.obj <- dw(x, eps = eps) plot(x) for(i in 1:dim(dw.obj)[1]){arc(dw.obj[i, 1:2], eps, dw.obj[i, 4:5], dw.obj[i, 6])} ## End(Not run) ```

### Example output

```
```

alphahull documentation built on June 22, 2019, 1:02 a.m.