# RMbessel

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Percentile

##### Bessel Family Covariance Model

RMbessel is a stationary isotropic covariance model belonging to the Bessel family. The corresponding covariance function only depends on the distance $r \ge 0$ between two points and is given by $$C(r) = 2^\nu \Gamma(\nu+1) r^{-\nu} J_\nu(r)$$ where $\nu \ge (d-2)/2$, $\Gamma$ denotes the gamma function and $J_\nu$ is a Bessel function of first kind.

Keywords
models, spatial
##### Usage
RMbessel(nu, var, scale, Aniso, proj)
##### Arguments
nu
a numerical value; should be equal to or greater than $(d-2)/2$ to provide a valid covariance function for a random field of dimension $d$.
var,scale,Aniso,proj
optional arguments; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.
##### Details

This covariance models a hole effect (cf. Chiles, J.-P. and Delfiner, P. (1999), p. 92, cf. Gelfand et al. (2010), p. 26). An important case is $\nu=-0.5$ which gives the covariance function $$C(r)=\cos(r)$$ and which is only valid for $d=1$. This equals RMdampedcos for $\lambda = 0$, there.

A second important case is $\nu=0.5$ with covariance function $$C(r)=\sin(r)/r$$ and which is valid for $d \le 3$. This coincides with RMwave. Note that all valid continuous stationary isotropic covariance functions for $d$-dimensional random fields can be written as scale mixtures of a Bessel type covariance function with $\nu=(d-2)/2$ (cf. Gelfand et al., 2010, pp. 21--22).

##### Value

RMbessel returns an object of class RMmodel

##### References

RMdampedcos, RMwave, RMmodel, RFsimulate, RFfit.

• RMbessel
• RMjbessel
##### Examples
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

model <- RMbessel(nu=1, scale=0.1)
x <- seq(0, 10, 0.02)
plot(model)
plot(RFsimulate(model, x=x))


Documentation reproduced from package RandomFields, version 3.1.36, License: GPL (>= 3)

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