R/fun_heavy_tailed.R

In fChange: Change Point Analysis in Functional Data

#' Simulate Heavy Tailed Independent Functional Data
#'
#' It generates a heavy tail independent functional observations of sample size n
#'
#' @param n Sample size of generated functional data. A strictly positive integer
#' @param nbasis Number of basis functions used to represent functional observations
#' @param df Degrees of freedom of the T-distribution to construct the functional
#' observations. The default value is 3
#' @param basis A functional basis object defining the basis. It can be the class of
#' \code{basisfd}, \code{fd}, \code{fdPar}. As a default it is set to be a Fourier basis
#' @param rangeval A vector of length 2 containing the initial and final values of the
#' interval over which the functional data object can be evaluated. As a default it is
#' set to be [0,1].
#' @param ... Further arguments to pass
#'
#' @import stats
#' @import fda
#' @export
#'
#' @return An independent functional data sample (class \code{fd}) containing:
#'\item{coefs}{
#' The coefficient array
#'}
#'\item{basis}{
#' A basis object
#'}
#'\item{fdnames}{
#' A list containing names for the arguments, function values
#' and variables
#'}
#'@details The implementation of this function is very similar to \code{\link{fun_IID}}. The heavy tail functional observations are generated
#'based on a linear combination of basis functions where the \eqn{i}-th linear combination coefficient has a t-distribution with \code{df} - degrees
#'of freedom.
#'
#'@references Ramsay, James O., and Silverman, Bernard W. (2006), \emph{Functional
#' Data Analysis, 2nd ed.}, Springer, New York.
#' @references Aue A., Rice G., Sonmez O. (2017), \emph{Detecting and dating structural breaks in
#' functional data without dimension reduction} (https://arxiv.org/pdf/1511.04020.pdf)
#' @seealso \code{\link{Data2fd}, \link{fun_IID}, \link{fun_AR}, \link{fun_MA}}
#' @examples fdata1 = fun_heavy_tailed(n=100, nbasis=25)
#' @examples fdata2 = fun_heavy_tailed(n=100, nbasis=25, df=4)
#'




fun_heavy_tailed <- function(n, nbasis, df=3, basis=NULL, rangeval=c(0,1), ...){
      if (is.null(basis)){
         basis = create.fourier.basis(rangeval = rangeval, nbasis=nbasis)
      }else{
         basis = basis
      }
      mdata = matrix(0, nbasis, n)
      for (j in 1:n){
         mdata[,j] = rt(nbasis, df)
      }
      fd(mdata, basis)
}