# exactHausdorff: The Hausdorff distances between the convex hulls of unions of... In disp2D: 2D Hausdorff and Simplex Dispersion Orderings

## Description

Given a sample x1,...,x_n, it is evaluated the distribution of the Hausdorff distances between xi + B(m,r) and xj + B(m,r) where: xi and xj are two different points from the sample; m is the sample mean of the xi's; r is a positive value and B(m,r) is the disc centered at m with radius r. The i-th point xi has probability prob[i].

## Usage

 `1` ```exactHausdorff(A, prob, r) ```

## Arguments

 `A` A matrix where each row corresponds with a different point. `prob` The probabilities of each row of A. If we are dealing with the empirical distribution then all points are equiprobable and prob = rep(1/nrow(A),nrow(A) `r` A positive number.

## Value

 `distance` The observed distances between xi + B(m,r) and xj + B(m,r) where: xi and xj are two different points from the sample. `probability` Probabilities of each distance. `alldistances` The whole set of distances with repetitions.

## Author(s)

Guillermo Ayala <[email protected]>

## References

Miguel Lopez-Diaz. An indexed multivariate dispersion ordering based on the Hausdorff distance. Journal of Multivariate Analysis, 97(7):1623 - 1637, 2006.

G. Ayala, M.C. Lopez-Diaz, M. Lopez-Diaz and L. Martinez-Costa. Methods and algorithms to test the simplex and Hausdorff dispersion orders with a simulation study and an ophthalmological application. Technical Report. 2012

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```library(disp2D) library(geometry) library(mvtnorm) sigma1 = matrix(c(0.912897,1.092679,1.092679,1.336440),byrow=TRUE,ncol=2) sigma2 = sigma1 + diag(1,ncol=2,nrow=2) A = rmvnorm(200,mean=rep(0,2),sigma=sigma1) B = rmvnorm(200,mean=rep(0,2),sigma=sigma2) r=.1 prob = probA = probB = rep(1/200,200) HA = exactHausdorff(A,probA,r) HB = exactHausdorff(B,probB,r) plot(HA\$distance, cumsum(HA\$probability), type = "l", xlab = "", ylab = "DF", xlim = range(c(HA,HB))) lines(HB\$distance, cumsum(HB\$probability), lty = 2) ```

disp2D documentation built on May 30, 2017, 12:09 a.m.