R: The Hausdorff distances between the convex hulls of unions of...
exactHausdorff
R Documentation
The Hausdorff distances between the convex hulls of unions of points
and disc centered at the mean.
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
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 <Guillermo.Ayala@uv.es>
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