Generates n realizations of a zero-mean Gaussian process. The function also accepts user-defined covariance functions (without "nugget" effect, see cov), The implemented defaults with scale parameter $$\phi$$, order $$o$$ and nugget effect variance $$\sigma^2$$ are:

• squared exponential covariance $$Cov(x(t), x(t')) = \exp(-(t-t')^2)/\phi) + \sigma^2 \delta_{t}(t')$$.

• Wiener process covariance $$Cov(x(t), x(t')) = \min(t',t)/\phi + \sigma^2 \delta_{t}(t')$$,

• Matèrn process covariance $$Cov(x(t), x(t')) = \tfrac{2^{1-o}}{\Gamma(o)} (\tfrac{\sqrt{2o}|t-t'|}{\phi})^o \text{Bessel}_o(\tfrac{\sqrt{2o}|t-t'|}{s}) + \sigma^2 \delta_{t}(t')$$

## Usage

tf_rgp(
n,
arg = 51L,
cov = c("squareexp", "wiener", "matern"),
scale = diff(range(arg))/10,
nugget = scale/200,
order = 1.5
)

## Arguments

n

how many realizations to draw

arg

vector of evaluation points (arg of the return object). Defaults to (0, 0.02, 0.04, ..., 1). If given as a single integer (don't forget the L...), creates a regular grid of that length over (0,1).

cov

type of covariance function to use. Implemented defaults are "squareexp", "wiener", "matern", see Description. Can also be any vectorized function returning $$Cov(x(t), x(t'))$$ without nugget effect for pairs of inputs t and t'.

scale

scale parameter (see Description). Defaults to the width of the domain divided by 10.

nugget

nugget effect for additional white noise / unstructured variability. Defaults to scale/200 (so: very little white noise).

order

order of the Matèrn covariance (if used, must be >0), defaults to 1.5. The higher, the smoother the process. Evaluation of the covariance function becomes numerically unstable for large (>20) order, use "squareexp".

## Value

an tfd-vector of length n

Other tidyfun RNG functions: tf_jiggle()