fda.usc: rproc2fdata – R documentation

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rproc2fdata

Simulate several random processes.

Description

Simulate Functional Data from different processes: Ornstein Uhlenbeck, Brownian, Fractional Brownian, Gaussian or Exponential variogram.

Usage

rproc2fdata(
  n,
  t = NULL,
  mu = rep(0, length(t)),
  sigma = 1,
  par.list = list(scale = 1, theta = 0.2 * diff(rtt), H = 0.5),
  norm = FALSE,
  verbose = FALSE,
  ...
)

Arguments

`n`	Number of functional curves to be generated.
`t`	Discretization points.
`mu`	`vector` which specifies the trend values at the discretization points, by default `mu`=μ(t)=0. If `mu` is a `fdata` class object, `t`=`argvals(mu)`.
`sigma`	A positive-definite symmetric matrix, Σ, specifying the covariance matrix among grid points. If `sigma` is a `scalar`, creates a random Gaussian process with Σ=`sigmaI` (by default `sigma=1`). If `sigma` is a `vector`, creates a random Gaussian process with Σ=`diag(sigma)`. If `sigma` is a character: create a random process using the covariance matrix Σ indicated in the argument, `"OU"` or `"OrnsteinUhlenbeck"`, creates a random Ornstein Uhlenbeck process with Σ(s,t)=σ^2/θ exp(-θ(s+t))(exp(2θ(s+t)-1)), by default θ=1/(3range(t)), σ^2=1. `"brownian"` or `"wiener"`, creates a random Wiener process with Σ(s,t)=σ^2 min(s,t), by default σ^2=1. `"fbrownian"`, creates a random fractional brownian process with Σ(s,t)=σ^{2H}/2{\|s\|^{2H}+\|t\|^{2H}-\|s-t\|^{2H}}, by default σ^2=1 and H=0.5 (brownian process). `"vexponential"`, creates a random gaussian process with exponential variogram Σ=σ^2 exp(-\|s-t\|/θ ), by default θ=.2range(t), σ^2=1*.
`par.list`	List of parameter to process, by default `"scale"` σ^2=1, `"theta"` θ=0.2 range(t) and `"H"`=0.5.
`norm`	If `TRUE` the norm of random projection is 1. Default is `FALSE`
`verbose`	If `TRUE`, information about procedure is printed. Default is `FALSE`.
`...`	Further arguments passed to or from other methods.

Value

Return the functional random processes as a fdata class object.

Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@usc.es

Examples

## Not run: 
par(mfrow=c(3,2))
lent<-30
tt<-seq(0,1,len=lent)
mu<-fdata(rep(0,lent),tt)
plot(rproc2fdata(200,t=tt,sigma="OU",par.list=list("scale"=1)))
plot(rproc2fdata(200,mu=mu,sigma="OU",par.list=list("scale"=1)))
plot(rproc2fdata(200,t=tt,sigma="vexponential"))
plot(rproc2fdata(200,t=tt,sigma=1:lent))
plot(rproc2fdata(200,t=tt,sigma="brownian"))
plot(rproc2fdata(200,t=tt,sigma="wiener"))
#plot(rproc2fdata(200,seq(0,1,len=30),sigma="oo")) # this is an error 

## End(Not run)

fda.usc

Functional Data Analysis and Utilities for Statistical Computing

v2.0.2

GPL-2

Authors

Manuel Febrero Bande [aut], Manuel Oviedo de la Fuente [aut, cre], Pedro Galeano [ctb], Alicia Nieto [ctb], Eduardo Garcia-Portugues [ctb]

Initial release

2020-02-17