rbpto  R Documentation 
Functions for simulation and computing theoretical values of a Boolean model with identically shaped grains with size given by a truncated Pareto distribution.
rbpto(lambda, grain, win, xm, alpha, lengthscales, seed = NULL, xy = NULL)
bpto.coverageprob(lambda, grain, xm, alpha, lengthscales = 1:500)
bpto.germintensity(coverp, grain, xm, alpha, lengthscales = 1:500)
bpto.covar(lambda, grain, xm, alpha, lengthscales = 1:500, xy)
lambda 
Intensity of the germ process (which is a Poisson point process) 
grain 
A single 
win 
The window to simulate in (an 
xm 
A parameter governing the shape of the Pareto distribution used  see details 
alpha 
A parameter governing the shape of the Pareto distribution used

lengthscales 
A list of scales of the 
seed 
Optional input (default in NULL). Is an integer passed to

xy 
A raster object that specifies pixel coordinates of the final
simulated binary map. It is used the same way as 
coverp 
Coverage probability of the Boolean model. 
The parameters xm
and alpha
are such that the CDF of the Pareto distribution is P(s <= x) = 1  (xm / x)^{alpha}
.
The distribution of grains scales is a stepfunction approximation to the CDF with steps at lengthscales
.
An owin
object.
rbpto()
: Simulate Boolean model with grain size distributed according to a truncated Pareto distribution.
bpto.coverageprob()
: The coverage probability of the Boolean model with grain size distributed according to a truncated Pareto distribution.
bpto.germintensity()
: The germ intensity of the Boolean model with grain size distributed according to a truncated Pareto distribution.
bpto.covar()
: The covariance of the Boolean model with grain size distributed according to a truncated Pareto distribution.
xy
is required to specify resolution and offset of pixel grid.
lambda < 0.2
win < square(r = 10)
grain < disc(r = 0.2)
xm < 0.01
alpha < 2
lengthscales < seq(1, 5, by = 0.1)
xi < rbpto(lambda, grain, win, xm, alpha, lengthscales = lengthscales)
# Compute properties of the Boolean model from parameters
bpto.coverageprob(lambda, grain, xm, alpha, lengthscales = lengthscales)
covar < bpto.covar(lambda, grain, xm, alpha, lengthscales = lengthscales,
xy = as.mask(win, eps = 2))
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